School Of Mathematics & StatisticsDual Honours Degrees

Faculty of Social Sciences

BA Accounting & Financial Management and MathematicsBSc Economics and MathematicsBA Business Management and Mathematics

Faculty of Arts and Humanities

BSc Mathematics and Philosophy

Faculty of Engineering

BSc Computer Science and MathematicsMComp Computer Science with Mathematics

Level Three and Level FourMathematics and Statistics Courses

2020/2021 and 2021/2022

Contents

1 Introduction 2

2 Disclaimer 3

3 Administrative Information 4Dates of Semesters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4Organisation of Modules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4Choice of Modules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4Unrestricted Modules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4Change of Choice of Modules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5Progression into the Third Year . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5Progression into the Fourth Year . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6Incorporating Employment into your Degree . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6Avoiding Collusion and Plagiarism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7Failure to Comply with Assessment Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . 10Statement on Assessment Criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11Award of Degrees . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12Classification of Honours Degrees . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12Transcripts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

4 Help, Guidance and Information 15Personal Tutors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15Higher Education Achievement Report . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15Library . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15Student Advice Centre, SSiD, Counselling Service, University Health Service . . . . . . . . . . . . . 17iSheffield . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17301 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17The English Language Teaching Centre (ELTC) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17What to do if things are not going right . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18Nightline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18The Careers Service . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18The Staff-Student Forum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19Study room . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19Voluntary work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20Where else to find Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20Office-holders in the School . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20Official University Information for Students on the Web . . . . . . . . . . . . . . . . . . . . . . . . 21

5 Health and Safety 22Smoking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22First Aid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22Fire Alarm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

6 Information on Mathematics and Statistics Courses 23The Aims and Learning Outcomes of the Degree Programmes . . . . . . . . . . . . . . . . . . . . 23Aims . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23Learning Outcomes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23Module Questionnaires . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23Degree Regulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24Specific degree regulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

7 Cover sheet arrangements 30

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1 Introduction

This handbook provides information of a general nature, and also information about coursestructures and individual modules, for students who expect to enter, in September 2020, thethird or fourth years of one of the following dual degree programmes that involve the Schoolof Mathematics and Statistics (SoMaS):

• the three-year BA Accounting & Financial Management and Mathematics programme;

• the three-year BSc Computer Science and Mathematics programme;

• the four-year MComp Computer Science with Mathematics programme;

• the three-year BSc Economics and Mathematics programme;

• the three-year BA Business Management and Mathematics programme;

• the three-year BSc Mathematics and Philosophy programme;

This booklet contains essential information to help you to make informed choices; it will beuseful throughout your third (and fourth) year. You are welcome to seek further informationor advice from your SoMaS Personal Tutor, the Senior Tutor, the Director of Teaching, or theSoMaS Programme Leader for your degree programme.

Dr. Simon Willerton, Director of Teaching, SoMaS

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2 Disclaimer

Every care has been taken to ensure the accuracy of the information in this booklet.To the best of our knowledge it was correct at the time at which it was prepared.The School of Mathematics and Statistics cannot accept responsibility for any errorswhich could occur should there be any further modification of the Regulations.

There have been a number of staff changes in the School in recent years with severalnew lecturers arriving and some older staff leaving. Further changes of this kindmay well occur. Courses at Levels 3 and 4 are specialized and the School cannotguarantee to run a course for which the qualified lecturer leaves. On the other handadditional options may be offered when staff with new interests arrive. Also, therecould be changes in the syllabus and timing, particularly of courses in 2021–2022.

In addition the School reserves the right to withdraw courses for which the numberof students registered is very low.

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3 Administrative Information

Dates of Semesters

Session 2020–2021

202028 September – 19 December Autumn Semester Teaching Period (12 weeks)

202118 January – 6 February Autumn Semester Examinations (3 weeks)8 February – 27 March Spring Semester, First Teaching Period (7 weeks)19 April – 21 May Spring Semester, Second Teaching Period (5 weeks)24 May – 12 June Spring Semester Examinations (3 weeks).

Organisation of Modules

Most Level 3 and 4 Mathematics and Statistics modules are delivered at the rate of 2 hoursof lectures per week. Your lecturers will make appropriate arrangements for times when youcan consult them.

Choice of Modules

Under the modular system all undergraduates must register each year for courses totalling 120credits. If you are registered for a dual degree programme then in your third year you willnormally take (about) 60 credits from each department contributing to the programme, butyou should check the Regulations for the programme.

You should make your choice of modules after you have received guidance from the SoMaSProgramme Leader for your degree programme, and from the other partner department.

Online module choice in 2020 runs from 18 May – 19 June. You should ensure that you submityour choice of modules during this period. Details of the operation of online module choicecan be found at http://www.sheffield.ac.uk/registration/continuing/module.

Unrestricted Modules

The term unrestricted means you are free to choose either a mathematics or a statistics moduleor one outside the School of Mathematics and Statistics. The marks from such modules areused in assessing your final degree classification.

It is your responsibility to determine the prerequisites and timetable for any non-mathematicalmodule and to obtain academic approval from the department which owns the module. Thetimetable for 2019–2020 is the best available guide, but this is subject to change for 2020–2021, and choices may need to be changed when the final timetable for 2020–2021 is knownin September.

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Note that some mathematics and statistics modules cannot be taken with certain modulesfrom other departments; details are included in the information on individual modules.

You may not generally choose Level 1 modules as unrestricted modules at Levels 2, 3 or 4; as anexception, modules from the Modern Languages Teaching Centre (MLTC) may be permitted.You are also advised that the School will not permit its students to take any mathematicsmodule from another University department as an unrestricted module at Level 2, 3 or 4.

Change of Choice of Modules

The University allows you to change your choice of modules in the first three weeks of anysemester. If you do change your options early in a semester it is your responsibility to ensurenot only that your timetable for that semester works but also that you will have suitable optionsavailable in future semesters for you to be able to complete your degree (for example, you willhave covered all prerequisites for your future choices). Change of choice of modules is doneonline.

The system can be accessed via MUSE. Log in as normal and go to the My Services tabthen Module Add/Drop for the link to the online system. Follow the simple instructions onscreen. Your core modules will already be listed when you access the online add/drop screens.Once you have entered and submitted your request to add and drop optional modules, yourdepartment will check and approve, or decline, your choices. You will receive an automatedemail, confirming when your record has been updated. If there are any problems with yourchoices, you will receive an email from your department advising you what action to take.

The online system is not available to distance learning students or to students taking modulesin the Institute of Lifelong Learning. They will need to use the paper ‘Add-Drop’ form. Add-Drop forms are available from the Student Services Information Desk (SSiD) in the Union ofStudents, and can also be downloaded from the SSiD web site at https://www.sheffield.ac.uk/ssid/forms. When you have completed the form, you must have it signed, to signifythe School’s approval, by the Programme Leader for your degree programme – see the “Makingchanges” section of https://sheffield.ac.uk/maths/current/admin. The form shouldthen be handed in at Hicks F10.

You can access the record of your choice of modules on central records. You must check thatthis record is correct in the fourth week of each semester. If it is not you will need to makethe appropriate changes online or using an Add-Drop form.

Progression into the Third Year

Since your Level 2 results contribute to your overall degree classification (unlike your Level 1results), the rules for progression from Level 2 into Level 3 are slightly more involved.

For students on BSc or BA degree programmes, the rules for progression from Level 2 toLevel 3 are given below, and apply to the January and June exams taken together:

(i) You may progress to Level 3 without any resit if you have obtained 120 credits in yourLevel 2 modules.

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(ii) The Examiners have discretion to decide whether students who have been awarded 100or 110 such credits may be deemed to have passed at Level 2 and permitted to proceedto Level 3. Permission to proceed in these circumstances is NOT automatic.

If you have obtained at least 100 credits but have failed one or two modules at Level 2,then you are strongly advised to resit any failed modules (even if the Examiners permityou to progress) as a pass would give you more flexibility in your third year, because inall cases there is a minimum number of credits that must be obtained (over the secondand subsequent years combined) if the degree is to be awarded.

(iii) If you have only 90 or fewer credits then you must resit ALL the modules you have failed.

Note that for any Level 2 module you are only allowed ONE resit attempt (not including casesfor which you are ‘Not Assessed’). If you are unable to pass Level 2 after the maximum numberof attempts at each module, you will not be able to continue with your degree.

If you wish to retake failed modules you should follow the instructions at https://www.

sheffield.ac.uk/ssid/assessment/resits-reassessment/ug. Any international stu-dent who wishes to take August 2021 resit examinations in their home country should applyto do so by the end of the Semester 2 examination period 2021. Further details can be found athttps://www.sheffield.ac.uk/ssid/assessment/resits-reassessment/overseas

The maximum score that can be credited as a result of a resit examination is 40.

Students on an MComp programme must obtain 120 credits at Level 2 with an average of atleast 54.5 to be permitted to progress to Level 3 of the same programme; those who do notmeet this requirement may be able to transfer to a BSc programme.

Progression into the Fourth Year

The Examiners may in their discretion recommend that a student on an MComp programmewho is awarded not fewer than 100 credits at Level 3 and who obtains a weighted mean gradeof not lower than 49.5 at Level 3 be permitted to proceed to Level 4.

This is not automatic, and students towards the bottom end of this region, or students withany fail marks, should not expect to be permitted to progress; experience has shown that suchstudents struggle with the additional difficulty of Level 4. If students are not permitted toprogress, then students may be eligible for a BSc degree.

A student who is permitted to progress from Level 3 to Level 4, with fewer than 120 creditsfrom the Level 3 year, may resit failed Level 3 modules once during the Level 4 year. The resitmark will be capped at 40 for modules with a 3** or a 3**** code, and at 50 for moduleswith a 4** or a 6**** code. If the resit mark is lower than the original, the higher mark willbe used in the final assessment.

Incorporating Employment into your Degree

The University of Sheffield recognises that both students and employers value the benefits thatstructured work experience can provide as part of a university degree programme. We havetwo options for incorporating a year in employment into your degree:

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(i) If you began your degree in Autumn 2018 or later, you may be able to transfer to one of ourfour “with Placement Year” programmes. In principle, this can be done at any point priorto your final year, subject to agreement by SoMaS. If you are in your penultimate year,you may need to find a placement before being allowed to transfer. These programmesincorporate extra support for finding a placement and developing employability skills,beyond those available to other undergraduates.

(ii) If you find a placement during your penultimate year, you can add “with EmploymentExperience” to any of our (non-Placement Year) programmes, subject to successful com-pletion of the placement. This requires transferring degree programmes, which needs tobe approved by SoMaS (and any other appropriate departments, for dual degrees).

Under either scheme, you will spend your penultimate year (i.e. the year between Levels 2and 3 of a three year degree, or between Levels 3 and 4 of a four year degree) in employment.Students typically return from their placement year confident and highly-motivated, often witha graduate job lined up for after their degree.

The placement should involve work connected with your degree programme or with your pro-posed future employment. We recognize that many mathematics graduates go into graduatejobs that do not use their degree directly. Therefore a placement with, for example, anaccountancy firm would be acceptable even if it did not involve the use of university-levelmathematics. Students need to find their own company placement and the SoMaS Employa-bility Lead needs to validate the placement. Mathematics students are very much in demandfor year-long placements, and many companies with interesting jobs for mathematicians arewilling to invest the training effort in year-long placements.

You will typically need to start planning for the placement a year before it starts. You areresponsible for getting the placement, but the Careers Service can assist. Those on thePlacement Year programme will also have help on offer from the Placement Year ProgrammeLead.

Your placement will be assessed on a pass or fail basis. It will not count towards your finaldegree classification; however, you will need to pass a formal assessment and complete theplacement year in order to gain the amended degree title. You will be required to completeand submit:

• A skills analysis (1600-2000 words), identifying specific skills that you have gained and/ordeveloped over the course of your placement,

• A reflection summary (600 words) summarising what you have achieved over the yearand lessons you have learned for the future.

For further details, see https://www.sheffield.ac.uk/careers/jobs/placements.

Avoiding Collusion and Plagiarism

This has been extracted from the University’s Guidance for Students on the Use of Un-fair Means, available from the SSiD web page at https://www.sheffield.ac.uk/ssid/

unfair-means.

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The University expects its graduates to have acquired certain attributes. Many of these relateto good academic practice.

Throughout your programme of studies at the University you will learn how to develop theseskills and attributes. Your assessed work is the main way in which you demonstrate that youhave acquired and can apply them. Using unfair means in the assessment process is dishonestand also means that you cannot demonstrate that you have acquired these essential academicskills and attributes.

What constitutes unfair means?

The basic principle underlying the preparation of any piece of academic work is that the worksubmitted must be your own work. Plagiarism, submitting bought or commissionedwork, double submission (or self plagiarism), collusion and fabrication of results arenot allowed because they violate this principle (see definitions below). Rules about these formsof cheating apply to all assessed and non-assessed work.

(i) Plagiarism (either intentional or unintentional) is using the ideas or work of anotherperson (including experts and fellow or former students) and submitting them as your own.It is considered dishonest and unprofessional. Plagiarism may take the form of cutting andpasting, taking or closely paraphrasing ideas, passages, sections, sentences, paragraphs,drawings, graphs and other graphical material from books, articles, internet sites or anyother source and submitting them for assessment without appropriate acknowledgement.

(ii) Submitting bought or commissioned work (for example from internet sites, essay“banks” or “mills”) is an extremely serious form of plagiarism. This may take the formof buying or commissioning either the whole piece of work or part of it and implies aclear intention to deceive the examiners. The University also takes an extremely seriousview of any student who sells, offers to sell or passes on their own assessed work to otherstudents

(iii) Double submission (or self plagiarism) is resubmitting previously submitted work onone or more occasions (without proper acknowledgement). This may take the form ofcopying either the whole piece of work or part of it. Normally credit will already havebeen given for this work.

(iv) Collusion is where two or more people work together to produce a piece of work, allor part of which is then submitted by each of them as their own individual work. Thisincludes passing on work in any format to another student. Collusion does not occurwhere students involved in group work are encouraged to work together to produce asingle piece of work as part of the assessment process.

(v) Fabrication is submitting work (for example, practical or laboratory work) any part ofwhich is untrue, made up, falsified or fabricated in any way. This is regarded as fraudulentand dishonest.

How can I avoid the use of unfair means?

To avoid using unfair means, any work submitted must be your own and must not include thework of any other person, unless it is properly acknowledged and referenced.

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As part of your programme of studies you will learn how to reference sources appropriatelyin order to avoid plagiarism. This is an essential skill that you will need throughout yourUniversity career and beyond. You should follow any guidance on the preparation of assessedwork given by the academic department setting the assignment.

You are required to declare that all work submitted is entirely your own work. Manydepartments will ask you to attach a declaration form to all pieces of submitted work (includingwork submitted online). Your department will inform you how to do this.

If you have any concerns about appropriate academic practices or if you are experiencing anypersonal difficulties which are affecting your work, you should consult your personal tutor,supervisor or other member of staff involved.

The following websites provide additional information on referencing appropriately and avoidingunfair means:

The Library provides online information literacy skills help https://www.sheffield.ac.

uk/library/idlt

The Library also has information on reference management software https://www.shef.

ac.uk/library/refmant/refmant.html

The English Language Teaching Centre operates a Writing Advisory Service throughwhich students can make individual appointments to discuss a piece of writing. This is availablefor all students, both native and non-native speakers of English. https://www.shef.ac.uk/eltc/languagesupport/writingadvisory/index

What happens if I use unfair means?

Any form of unfair means is treated as a serious academic offence and action may be takenunder the Discipline Regulations. For a student registered on a professionally accreditedprogramme of study, action may also be taken under the Fitness to Practise Regulations.Where unfair means is found to have been used, the University may impose penalties rangingfrom awarding no grade for the piece of work or failure in a PhD examination through toexpulsion from the University in extremely serious cases.

Detection of Unfair Means

The University subscribes to a national plagiarism detection service which helps academic staffidentify the original source of material submitted by students. This means that academic staffhave access to specialist software that searches a database of reference material gathered fromprofessional publications, student essay websites and other work submitted by students. It isalso a resource which can help tutors and supervisors to advise students on ways of improvingtheir referencing techniques. Your work is likely to be submitted to this service.

For further information, see https://www.sheffield.ac.uk/ssid/complaints-and-appeals.

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Failure to Comply with Assessment Requirements

Failure to attend an examination without adequate reason will result in a grade of 0 beingawarded. If you have good reasons to miss an exam due to circumstances beyond yourcontrol, you need to fill in an Extenuating Circumstances Form: https://www.sheffield.

ac.uk/ssid/forms/circs. If the circumstances are medical and you are registered with theUniversity Health Service (UHS), note what it says about filling in the electronic (or mobileapp) version of the form and submitting it for UHS to add the documentation, and also that thedoctor needs to have seen you while you are ill. (See the explanatory notes for this and more.The notes can be found here: https://www.sheffield.ac.uk/ssid/forms/circsnotes)In all other cases, please take the completed form and any other supporting documentationto SoMaS Reception in F10 as soon as you reasonably can. If you become ill during an exam,please tell an invigilator.

Excuses such as misreading the timetable or oversleeping are not acceptable as reasons forabsence, but any student who misses an exam for such a reason should report to SoMaSReception in F10 as soon as possible.

All unauthorized material (such as revision notes, books, etc) must be left outside the ex-amination hall. This includes notes on scraps of paper. Students should ensure that theirpockets are empty of such notes before entering the examination room. Students must alsoensure that there are no written notes on their hands when they enter the examination halland must not write on their hands during an examination. For further details of examinationprocedures, students should consult the regulations on examinations, which can be found viathis link: https://www.sheffield.ac.uk/ssid/exams/rules/index

It is recommended that any student with personal circumstances continuing from the previoussemester submits a new Extenuating Circumstances Form, to keep us up-to-date and to ensurethat their case is not overlooked. Any student with a disability or chronic medical condition,for whom the Disability and Dyslexia Support Service has produced a learning support plan,need not keep filling in forms to inform us of their condition. In fact, disabilities and chronicmedical conditions are not normally regarded as extenuating circumstances, the emphasis beingon providing support to help students to do the best they can. However, it may be appropriateto submit an Extenuating Circumstances Form if there is a particular flare-up or complicationat a time affecting exams.

Failure to hand in assessed coursework on time without good reason will result in the impositionof a penalty in accordance with the University’s Penalties Policy. Late submission of a majorpiece of assessed coursework, such as a project dissertation, will result in the deduction of5% of the total mark awarded for each of the first 5 ‘University Working Days’ by which thesubmission is late; work submitted even later than that will receive a mark of 0. For piecesof assessed coursework that contribute only a small percentage of the overall assessment, theFaculty of Science has given the School approval to operate a policy of ‘zero tolerance’, underwhich any late submission receives a mark of 0.

Module leaders have the power to award dispensations in cases where the lateness was causedby certifiable medical problems or severe personal circumstances; requests for such dispensa-tions should be made as soon as the problem is known, in writing or by e-mail to the moduleleader; students making such requests must also complete an ‘Extenuating CircumstancesForm’ and hand it in at SoMaS Reception (F10).

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Statement on Assessment Criteria

Typical examinations in SoMaS involve several questions, each of which will have componentsof at least some of the following types: (i) explanation of theory developed in the module; (ii)standard problems solvable using methods seen in the module; (iii) more difficult unseen prob-lems requiring knowledge of the module but also requiring some original thought. Students’scripts are assessed using a strict and detailed marking scheme, usually based on method andaccuracy marks. The primary criterion is correctness, whether it be of calculation, method orexplanation.

This produces a set of ‘raw marks’ which is then scaled, using the judgement of the examiner,to the University’s 100-point reporting scale, which corresponds to degree classifications usingthe following rule:

70–100 : Class I60–69 : Class II(i)50–59 : Class II(ii)45–49 : Class III40–44 : Pass.

If an examiner feels that a mark of 30% on the exam is deserving of a pass, then 30% willbe scaled to 40 on the University’s scale; there are similar points at each of the classificationboundaries. The scaling is subjected to a central School scrutiny process involving the pastrecord of each student who is registered for the module and for whom there are no abnormalcircumstances.

Examination papers, including the past papers to which the students have access in advance,carry the distribution of marks between parts of questions.

The internal checker for each examination paper and the appropriate External Examiner areprovided with copies of the module’s objectives/learning outcomes, and these are also dis-tributed to students.

The School operates a scheme whereby marking is checked for accuracy. In addition, on eachpaper at Level 2 and above selected scripts, usually from the border bands between classifi-cations, are sent to the appropriate External Examiner. Before the Final Year ExaminationBoard Meeting, the External Examiners have the opportunity to look at all final year scripts,and generally look at those of candidates that are very close to borderlines, as well as otherspecial cases.

All examination marking and all discussion at formal Examination Board Meetings is conductedanonymously, that is, students are identified only by their registration numbers.

Students have the right to see their examination scripts after they are marked; this generallytakes place around Week 3 of Semester 1 (for the previous session’s June exams) and Week 6of Semester 2 (for the January exams).

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Award of Degrees

In order to qualify for the award of a degree, students have to obtain a specified number ofcredits. Also, the ‘level’ of the credits is important. In what follows, ‘Level 3 modules’ refers tocourses MAS3** (and courses of a similar level in other departments), normally taken duringLevel 3, and ‘Level 4 modules’ refers to courses MAS4** (and courses of a similar level inother departments), normally taken during Level 4. The pass mark for Level 3 modules is 40,and the pass mark for Level 4 modules is 50.

In order to be awarded an honours degree of BA or BSc, you must obtain at least 200credits, of which at least 90 must be of Level 3 modules, out of the overall 240 credits possibleon the second and third years combined.

This is a minimum requirement below which you cannot obtain an honours degree: the grantingof a pass degree (that is, without honours) to a student with fewer than 200 credits (or withfewer than 90 credits at Level 3 modules) is always at the discretion of the examiners, andrequires the specific concurrence of the External Examiners. A minimum of 180 credits isrequired for this.

Candidates for a BA or BSc degree who have completed, and submitted themselves for assess-ment on, 120 credits at each of Levels 2 and 3 but have not been recommended for the awardof a degree may enter for a subsequent examination for each failed module on one furtheroccasion (subject to a maximum of two opportunities to sit any given module), but will onlybe eligible for the award of a pass degree.

In order to be awarded an honours degree of MComp, you must obtain at least 320 credits,of which at least 90 must be Level 4 modules, out of the overall 360 credits possible onthe second, third and fourth years combined, provided the Examiners recommend a classII(ii) degree or above. (Classification of honours degrees is discussed in the next subsection.)Candidates whom the Examiners would place in Class III will be recommended for the awardof a BA or BSc degree with honours; candidates whom the Examiners deem to be worthy ofa pass shall be recommended for the award of a BA or BSc pass degree.

In particular, in order to be awarded an MComp degree, you must pass at least 90 credits ofLevel 4 modules.

Candidates for an MComp degree who have completed, and submitted themselves for assess-ment on, 120 credits at each of Levels 2, 3 and 4 but have not been recommended for theaward of a degree may enter for a subsequent examination for each failed Level 4 module onone further occasion (subject to a maximum of two opportunities to sit any given module),but will only be eligible for the award of a BSc pass degree.

Classification of Honours Degrees

Under the current Regulations, for each module you complete you will be awarded a mark onthe University 100-point scale. This subsection describes the way that these marks contributeto the final degree classification.

The full details are available from the University’s General Regulations for First Degrees athttps://www.sheffield.ac.uk/polopoly_fs/1.743323!/file/22_Reg_XV_General_Regulations_

for_First_Degrees.pdf Here are the main points.

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All your module marks (including any for which the mark is a fail) for years 2, 3 (and 4 ifappropriate) are averaged, but Level 2 marks are given half the weight of Level 3 and Level 4marks. Then two calculations are made.

Calculation 1 (the weighted mean grade) is made in accordance with the following principles:

• where a candidate’s weighted mean grade is of a value indicated in the first column, theoutcome of Calculation 1 shall be the corresponding class indicated in the second column

69.5 or higher : Class I59.5 or higher : Class II(i)49.5 or higher : Class II(ii)44.5 or higher : Class III39.5 or higher : Pass;

• where a candidate’s weighted mean grade falls within the band indicated in the firstcolumn, the outcome of Calculation 1 shall be the borderline to the corresponding classindicated in the second column

68.0–69.4 : Class I58.0–59.4 : Class II(i)48.0–49.4 : Class II(ii)43.5–44.4 : Class III38.0–39.4 : Pass.

Calculation 2 (the distribution of grades) is made in accordance with the following principles:

• where the best half of a candidate’s weighted grades are of a value indicated in the firstcolumn, the outcome of Calculation 2 shall be the corresponding class indicated in thesecond column

69.5 or higher : Class I59.5 or higher : Class II(i)49.5 or higher : Class II(ii)44.5 or higher : Class III39.5 or higher : Pass;

• where the best five twelfths of a candidate’s weighted grades are of a value indicated inthe first column, the outcome of Calculation 2 shall be the borderline to the correspondingclass indicated in the second column above.

In recommending the class of degree to be awarded to each candidate, the Examiners shall takeinto account the outcomes of Calculations 1 and 2 in accordance with the following principles:

• where one Calculation places the candidate in one class and the other Calculation placesthe candidate in either the same class or the borderline to the same class, the candidateshall normally be recommended for the award of a degree of that class;

• where one Calculation places the candidate in one class, and the other Calculation placesthe candidate in the borderline to the class immediately above, the candidate shall nor-mally be recommended for the award of a degree of the lower class;

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• where one Calculation places the candidate in one class, and the other Calculation placesthe candidate in the class immediately below, the candidate shall be considered as beingin the borderline to the higher class, and the class of the degree to be recommended bythe Examiners shall normally correspond to the class indicated by the weighted mean ofthe grades at the final Level of study;

• where both Calculations place the candidate in the same borderline, the class of the degreeto be recommended by the Examiners shall normally correspond to the class indicated bythe weighted mean of the grades at the final Level of study;

• where one Calculation places the candidate in one class, or borderline to a class, and theother Calculation places the candidate in another class, or borderline to a class, neitherimmediately above nor below, the Examiners shall recommend the classification which,having regard to all the evidence before them, best reflects the overall performance ofthe candidate.

Note that the Examiners are free to vary from the formal rules for any candidate where there isstrong evidence to support such a decision. In consideration of such evidence, the Examinerswill seek guidance from the School’s External Examiners. Also, if a candidate is awarded aclassified degree (I, II(i), II(ii), or III) then the degree is an honours degree irrespective ofwhether the candidate has any failed modules.

There is a University appeals procedure, full details of which are displayed on the studentnotice boards listed later in this handbook. They may be also found on the web at https:

//www.sheffield.ac.uk/ssid/complaints-and-appeals.

Transcripts

After graduation, you may wish to obtain a transcript of your detailed module results to showprospective employers. For details see https://www.shef.ac.uk/ssid/transcript. Notethat there is a small charge, which increases more than 12 months after graduation.

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4 Help, Guidance and Information

Personal Tutors

The SoMaS personal tutorial system operates for the rest of your course. The present ar-rangements are that students normally continue with the same SoMaS personal tutor as inthe second year. If you envisage any problem with this then please see the Senior Tutor; itis possible for you to request a change of personal tutor. Third- and fourth-year studentsshould go to see their tutors each semester, at the beginning of Semester 1 and in Semester 2when the Semester 1 examination results have been published. However, questions about workconcerning particular courses should generally be put to the lecturers concerned. All studentsare encouraged to keep in touch with their tutors who are then in a good position to act asreferees when the time for job applications arrives.

There is in addition a Tutor for Men Students, who is available to discuss problems of a morepersonal or confidential nature. The Senior Tutor acts as a Tutor for Women Students.

If you have any difficulty in contacting your personal tutor, or he or she is unable to solveany problem or answer any query, then you can approach the Senior Tutor or the ProgrammeLeader for your degree programme or other designated staff members (see the list at http:

//www.maths.dept.shef.ac.uk/maths/contact.html).

Please make sure that your home address is correct on MUSE before you leave at the endof Semester 2. You will have the same University e-mail address in 2020–2021 as this year.You should make sure your tutor knows your e-mail address, and you should check for e-mailmessages when you return to Sheffield in September.

Higher Education Achievement Report

The University has introduced a new kind of degree transcript for all new undergraduate stu-dents: the Higher Education Achievement Report or ‘HEAR’. The HEAR provides a compre-hensive record of your university achievements and it recognises your extra-curricular achieve-ments as well as your academic learning. It can be used to help you identify your strengths,and to plan how to build on these to achieve your goals, and it provides employers and otherswith evidence of your university learning and experiences.

Find out more by visiting the HEAR website https://www.sheffield.ac.uk/ssid/hear

Library

The University Library provides 24-hour access to study space, a huge range of books andonline information (including online journals and ebooks) as well as advices to help you findand use information effectively. You will find all the information you need to get started onthe library webpages.

Places to study

There are four different library sites where you can go to study, find reading for your course,and get advice on finding, organising and referencing information. You will need to bring your

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Ucard with you to get into the library, borrow books and to use the printers and copiers.Remember to ask a member of staff if you need anything.

• The Information Commons (IC) is open 24 hours a day. You should find most of yourrecommended books here. Visit the Information Desk on level 1 for help using the library,finding materials for your course, or for help with your computer or laptop.

• The Diamond is open 24 hours a day, and has four floors of study space. Visit the topfloor (Level 4) to speak to Library and CiCS staff at the Information Desk or to use thecollection of reference books.

• Western Bank Library is a good place for quiet study or revision, with a large readingroom overlooking Weston Park.

• The Health Sciences Library, based in the Medical School at the Royal Hallamshire Hos-pital has books and journals covering medicine, dentistry and health.

Visit the learning spaces page (https://www.sheffield.ac.uk/learning-spaces) to checkhow busy each library is before you go and see the other study spaces available across campus.

StarPlus is the Library’s online search tool. Use it to find books and ebooks, online journals,articles, and other information available through the Library. Log in to MUSE and openStarPlus from the link in the ‘My Services’ menu. Use StarPlus to:

• find reading for your course or research for an assignment

• request something that is out on loan; the Library will let you know when it is ready tocollect

• save the details of useful books, journals and articles so you can refer to them later (usefulwhen referencing)

Searching the scientific literature

Web of Science and Scopus and arXiv.org can be used to search the journal literature andexplore scientific research. To find other useful databases, visit the Maths and Statistics libraryguide, or contact your librarian.

Developing your skills: visit the Library’s study web pages for advice on:

• how to find information for your study and assignments,

• how to cite/reference correctly, and avoid plagiarism

• finding details of optional workshops to support your learning

Help and support

• For general enquiries, contact Library Help or speak to a member of library staff.

• Oliver Allchin is the librarian for Science – you can contact him for advice on findingreading for your studies or with any other questions you have relating to library supportfor your course (o.allchin@sheffield.ac.uk, 01142227333, book an appointment)

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• If you would like to borrow a book or read an article that the Library does not have,complete the InterLibrary Request form (available from the ‘My Services’ menu in MUSE)and we will try to get it for you from the British Library. If you would like to suggest abook for the Library to buy use the book recommendation form.

Student Advice Centre, SSiD, Counselling Service, University Health Service

The Student Advice Centre (https://www.sheffield.ac.uk/ssid/contacts/advice) andStudent Services Information Desk (SSiD, https://www.sheffield.ac.uk/ssid) provideassistance on a wide range of problems. Specifically, they provide advice on housing, finance,problems about harassment, and help to international students; they also help with academicmatters. The Counselling Service (https://www.sheffield.ac.uk/ssid/counselling)and the University Health Service (https://www.sheffield.ac.uk/ssid/health-service)are also there to help you, and help with mental health problems can be found from https://

www.sheffield.ac.uk/ssid/health-service/conditions/mental-health; strict con-fidence is always observed.

iSheffield

Lots of information can be found from the iSheffield mobile app (see https://www.sheffield.ac.uk/it-services/isheffield). In particular your timetable should be there, and nearthe start of semester it should have the correct tutorial times and rooms for you.

301

301: Student Skills and Development Centre offers a range of services for all students:

• Maths and Statistics Help

• Academic Skills workshops

• Study Skills Sessions

• Specialist Dyslexia/SpLD tutorial Service

• Languages for All programme

• Writing Advisory Service

301 also offers an Academic Skills Certificate which can be included in your Higher EducationAchievement Report (HEAR). For more details see https://www.sheffield.ac.uk/ssid/

301/services .

The English Language Teaching Centre (ELTC)

If you need help with your English language then this can be provided by the ELTC. For furtherdetails see https://www.sheffield.ac.uk/eltc.

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What to do if things are not going right

Obviously, the School hopes that all of you will enjoy your degrees and your time in Sheffield.But we know that, for various reasons, some of you may have problems which may affect yourstudies, and that at times there are things which need to take precedence over your work.

Your first port of call within SoMaS should be your Personal Tutor, or the Senior Tutor. Wemay not be qualified to give you the help that you may need, but the University will havepeople who can, and your tutor can direct you to the appropriate help. There is a StudentAdvice Centre next to the Student Services Information Desk in the Student Union, who have alot of leaflets and can also help advise you. See https://www.sheffield.ac.uk/ssid/sos

for a range of services offered by the University.

For any issues that affect assessment, you need to complete an Extenuating CircumstancesForm – see page 10.

If issues persist, or are very serious, you may want to take Leave of Absence, and return at alater date. For this, you will need to complete a Change of Status Form for Leave of Absence.Some issues are discussed at https://www.shef.ac.uk/ssid/change-of-status/leave;for example, there are likely to be some financial considerations, and overseas students mayface visa issues. If medical issues are the cause of the request, you will need to satisfy theUniversity that you have recovered sufficiently before you return. Any forms which affect your“status” will require the signature of the Senior Tutor; they should then be handed in at SoMaSReception (F10) so that we can make a copy, before being sent to Taught Programmes Office.

All forms can be downloaded from https://www.sheffield.ac.uk/ssid/forms; papercopies of all these are also available from SoMaS Reception (F10).

Nightline

Nightline (see https://www.sheffieldnightline.co.uk) is the University of Sheffield’sconfidential listening and information telephone service. It is run by trained student volunteers,and operates from 8.00pm until 8.00am every night during term time. It offers studentseverything from the phone number of a twenty-four hour taxi company, to examination dates,times and locations, and information about many issues that can be encountered within studentlife. It provides a vital support network for all students, so whatever you need to say, Nightlineis listening, and the service can be called free from phones in halls of residence. If you think youwould like to volunteer for Nightline, contact sunl@sheffield.ac.uk for more information.

The Careers Service

The Careers Service (whose web page is at https://www.shef.ac.uk/careers/) offers anexcellent provision, backed up with a wealth of experience, to help students decide on a careerand to find employment after graduation. You could also talk to the School’s Careers Officer,listed on http://www.maths.dept.shef.ac.uk/maths/contact.html.

Making good career decisions will involve you in thinking about your qualities and inclinations.The Careers Service provide resources on career planning, CV writing, job seeking, interviewskills, and much else. They also organise an extensive programme of careers events, which

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provides valuable opportunities to meet prospective graduate employers, and find out whatskills they are looking for.

Graduates from our degrees go on to a wide range of careers. Many go on to careers for whicha mathematical degree is very important; others go on to careers where degree-level educationis important, though not necessarily using mathematical skills. Mathematics graduates havea strong range of transferable skills, including excellent numeracy and analytical problemsolving skills. Your degrees often make use of computer packages, and these IT skills areoften adapatable to IT requirements of employers. Employers also value highly the ability tocommunicate mathematical ideas to lay audiences.

A number of our graduates have interest in teaching; the Postgraduate Diploma in Education(PGDE) is a common qualification, and is offered in mathematics by the University of Sheffield(and many other universities). It is administered by the School of Education, and you shouldcontact them for further information. Other graduates go on to more specialised postgraduatequalifications, including our own MSc in Statistics and MSc in Mathematics.

Students are strongly advised to make use of the wide range of resources that the CareersService has to offer. The Careers Service (https://www.sheffield.ac.uk/careers) islocated at 241 Glossop Road in Edgar Allen House. There is also a Student Jobshop in theStudent Union.

The School of Mathematics and Statistics runs MAS279 (Career Development Skills), a ded-icated careers module for Mathematics students, which is available to students on a numberof our single honours programmes.

The Staff-Student Forum

Nominations for the Staff-Student Forum will first be requested in the Spring Semester, forpositions in the following academic year. Please think about the possibility of serving on theForum. It will give you an opportunity to have a role in the organisation and management offactors influencing student life in the School of Mathematics and Statistics. The Forum usuallymeets twice a semester. A number of student members serve as student representatives onthe School Teaching Committee.

Issues may be raised with forum members at any time. You can find more information athttps://www.sheffield.ac.uk/maths/current/representation, where you can alsofind a feedback form which goes to SoMaS Reception and eventually to the Director of Teach-ing.

There are further opportunities for student representation within the Faculty of Science.

Study room

I19 Hicks, on the 5th floor, is a study room for undergraduates. It has plenty of space, tablesand chairs and a whiteboard, and is intended for quiet study. It is somewhere you can go tomake productive use of time in between lectures and tutorials, and might be especially usefulif you are in the Hicks Building and you do not want to use time going to the InformationCommons, Library, Student Union or wherever. There is a smaller room, the Barry JacksonRoom, at the back of the ground floor of the building, just before Lecture Rooms 3 and 4.

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This is also somewhere you can go to sit down, but with maybe less of an expectation of peaceand quiet, more a social space.

Voluntary work

The University encourages its students to consider undertaking some voluntary work. Thetext below has been provided by the Manager of Sheffield Volunteering, which is based in theStudents’ Union.

‘Volunteering is a great way to get to know the city and its people. You cangain career-related experience or simply volunteer for something that appeals.

‘You can do something just for a day or give a couple of hours each weekor fortnight. It’s really flexible and you won’t be asked to help during exams orvacations.

‘Choose from over 100 options — in student neighbourhoods and the city centre.Alternatively, we can help you to develop your own volunteer project involving otherstudents and benefiting the wider community.

‘Our staff can help you to find something that’s right for you. Training andout-of-pocket expenses are provided too.

‘Set yourself apart. Visit https://www.sheffield.ac.uk/experience/volunteeror see us in the Source (Level 3, Union Building).’

Where else to find Information

Information will be displayed in the Hicks Building on the notice boards outside F10.

Urgent messages will be displayed in the Entrance Foyer, or sent by e-mail. Please checknotice boards and your e-mail regularly.

Office-holders in the School

A list of the members of staff who currently hold various offices in the School of Mathemat-ics and Statistics can be found at http://www.maths.dept.shef.ac.uk/maths/contact.html.

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Official University Information for Students on the Web

General regulations (including degree regulations) https://www.shef.ac.uk/calendar/

General Regulations relating to Academic Appeals https://www.sheffield.ac.uk/polopoly_fs/1.743227!/file/27_Reg_XX_General_Regulations_relating_to_Academic_Appeals.

pdf

Regulations and procedures for grievances and complaints, Appeals https://www.sheffield.ac.uk/ssid/complaints-and-appeals

Specific SoMaS programme regulations https://www.shef.ac.uk/calendar/regs

SSiD web pages (including exam information, fees, finance, etc.) https://www.shef.ac.

uk/ssid/

LeTS (Learning and Teaching Services) https://www.shef.ac.uk/lets/

CICS IT information for students https://www.sheffield.ac.uk/it-services/students

Student Rights and Responsibilities https://www.sheffield.ac.uk/ssid/ourcommitment/rights

Help and support for students https://www.shef.ac.uk/ssid/sos/

Disability and dyslexia support https://www.sheffield.ac.uk/ssid/disability

Essential guide for mature students https://www.sheffield.ac.uk/ssid/mature-students

Information for international students https://www.shef.ac.uk/ssid/international/

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5 Health and Safety

Smoking

Students are reminded that smoking is prohibited on all University premises – this includes thearea under the canopy at the main entrance to the Hicks Building. In addition, we requestthat you refrain from smoking on the steps immediately outside the Hicks Building.

First Aid

First Aid boxes are available in SoMaS Reception (Room F10) and the Porters Lodge (HicksFoyer, D Floor). Lists of qualified first-aiders can be found outside, or near to, these locations.

Fire Alarm

If the fire alarm sounds in the Hicks Building, please proceed calmly to the nearest exit andassemble in the designated area (on the concourse, underneath the road bridge). Do notuse lifts. Do not re-enter the building until you have been told that it is safe to do so by afire officer. Weekly fire alarm tests are performed in all University buildings at varying timesdepending on the building. On these occasions the bell rings for approximately 15-30 secondsand no action is required unless the alarm sounds continuously for longer than approximately30 seconds. The test will take place in the Hicks Building on Wednesdays at about 9.30.

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6 Information on Mathematics and Statistics Courses

The Aims and Learning Outcomes of the Degree Programmes

The mission of the School of Mathematics and Statistics is

• to conduct high quality research in mathematics and statistics;• to provide an excellent and inspiring education for students;• to support, to promote and to increase the impact of our disciplines;• to be a research-led school that maintains high standards in all activities.

Aims

For all the School’s undergraduate programmes, the aims are:

• to provide an intellectual environment conducive to learning;• to prepare students for careers that use their mathematical and/or statistical training;• to provide teaching that is informed and inspired by the research and scholarship of the

staff;• to provide students with assessments of their achievements over a range of mathematical

and statistical skills, and to identify and support academic excellence.

For its dual degree programmes, the School aims to provide an appropriate Mathematicscomponent.

Learning Outcomes

In line with the requirements of HEFCE’s Teaching Quality Information initiative, the Uni-versity has introduced programme specifications for undergraduate and postgraduate taughtprogrammes to provide clear and explicit information for existing and potential students sothat they can make informed choices about their studies. In addition to the Aims of theSchool’s undergraduate programmes listed above, there are Learning Outcomes that studentsare expected to have developed upon successful completion of the programme and achieve-ment of which will usually have been demonstrated via the assessment process. These dif-fer for each degree programme offered; students may consult the latest versions at https:

//www.shef.ac.uk/calendar/progspec.

Module Questionnaires

Students are strongly encouraged to complete Module Questionnaires for every module theytake. These questionnaires are now administered electronically, and instructions on how tocomplete the questionnaires will be issued every semester.

These questionnaires are important to the School. This is your formal opportunity to giveyour view on aspects of the course – you can also give comments informally via your PersonalTutor, the Staff-Student Forum, to the lecturer directly, etc., and this is also appreciated.

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We are always keen to hear ways to improve our teaching and your learning experience. Con-sidered and thoughtful feedback can provide an extremely helpful input into the School’steaching.

In the same way that receiving a piece of marked work with just a mark out of 10 is not as usefulas comments showing how you can improve, we would like to encourage you to be specificand constructive in your questionnaire responses. Reasoned and constructive comments youmake on modules can be very helpful, both to the individual lecturer concerned, and to theSchool, so that we can spread good practice.

Lecturers are human beings with feelings, just like students, and if you feel the need to becritical of aspects of a module, please try to offer criticism in a sensitive way. It is alwaysgood to read positive comments as well as critical ones, so if you feel that a lecturer is doingsomething well, please let them know!

The questionnaires and comments are considered by members of the Staff-Student Forum, andby the School’s Teaching Committee. Comments have led to changes in School procedures,as well as to alterations in course content and practice of lecturers. They also form a valuableinput to the annual appraisal of staff.

Questionnaire results (and any lecturer responses) are published on the Staff-Student ForumMOLE page, where they may be viewed by all SoMaS students. Your responses can help thoseat lower levels make their module choices. Your considered feedback plays a valuable part inimproving our teaching.

Degree Regulations

Full details of these Regulations are available on the web, as described in the section entitled‘Official University Information for Students on the Web’ on p.21. However, at the time ofpublication of this handbook, the Regulations on the web may be for 2019–2020 rather than2020–2021. In particular, their lists of modules may reflect availability in 2019–2020 ratherthan in 2020–2021.

This booklet lists the relevant Mathematics and Statistics modules, but not those from thepartner departments in these degrees. The requirements laid down for those other subjects arecontained in the University Regulations. You must consult the other department for details ofcompulsory modules and possible options. You must take care in choosing your modules tocheck that you have the relevant pre-requisites. You should also be careful to avoid timetableclashes.

You are reminded that, to be eligible to enter Level 3 of an integrated masters programmesuch as MComp, you must normally have obtained 120 credits at Level 2 with an averageof at least 54.5. Candidates for such a degree who fail to achieve the required 54.5 averagein Level 2 should discuss the situation with the SoMaS Programme Leader for their degreeprogramme.

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Specific degree regulations

BA Accounting & Financial Management and Mathematics (MGTU14) Year 3

Candidates for this degree must take

(a) modules to the value of 40 credits chosen from the following list of Level 3 MAS modules:

MAS302 Undergraduate Ambassador Scheme in Mathematics 20 creditsMAS322 Operations Research 10 creditsMAS330 Topics in Number Theory 10 creditsMAS332 Complex Analysis 10 creditsMAS334 Combinatorics 10 creditsMAS341 Graph Theory 10 creditsMAS343 History of Mathematics 10 creditsMAS345 Codes and Cryptography 10 creditsMAS360 Practical and Applied Statistics 20 creditsMAS361 Medical Statistics 10 creditsMAS362 Financial Mathematics 10 creditsMAS364 Bayesian Statistics 10 creditsMAS367 Linear and Generalised Linear Models 10 creditsMAS369 Machine Learning 10 creditsMAS370 Sampling Theory and Design of Experiments 10 creditsMAS371 Applied Probability 10 creditsMAS372 Time Series 10 credits

(b) modules to the value of 40 credits provided by the Management School as laid down inthe University Regulations;

(c) modules to the value of 40 credits chosen from the above Level 3 MAS modules, additionalmodules provided by the Management School as laid down in the University Regulations,and unrestricted modules, with no more than 20 credits of unrestricted modules.

BA Business Management and Mathematics (MGTU13) Year 3

Candidates for this degree must take

(a) modules to the value of 40 credits chosen from the following list of Level 3 MAS modules:

MAS302 Undergraduate Ambassador Scheme in Mathematics 20 creditsMAS322 Operations Research 10 creditsMAS330 Topics in Number Theory 10 creditsMAS332 Complex Analysis 10 creditsMAS334 Combinatorics 10 creditsMAS341 Graph Theory 10 creditsMAS343 History of Mathematics 10 credits

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MAS345 Codes and Cryptography 10 creditsMAS360 Practical and Applied Statistics 20 creditsMAS361 Medical Statistics 10 creditsMAS362 Financial Mathematics 10 creditsMAS364 Bayesian Statistics 10 creditsMAS367 Linear and Generalised Linear Models 10 creditsMAS369 Machine Learning 10 creditsMAS370 Sampling Theory and Design of Experiments 10 creditsMAS371 Applied Probability 10 creditsMAS372 Time Series 10 credits

(b) modules to the value of 40 credits provided by the Management School as laid down inthe University Regulations;

(c) modules to the value of 40 credits chosen from the above Level 3 MAS modules, additionalmodules provided by the Management School as laid down in the University Regulations,and unrestricted modules, with no more than 20 credits of unrestricted modules.

BSc Computer Science and Mathematics (COMU109) Year 3

Candidates for this degree must take

(a) modules to the value of between 40 and 80 credits chosen from the following list of Level3 MAS modules:

MAS302 Undergraduate Ambassador Scheme in Mathematics 20 creditsMAS322 Operations Research 10 creditsMAS325 Mathematical Methods 10 creditsMAS330 Topics in Number Theory 10 creditsMAS331 Metric Spaces 10 creditsMAS332 Complex Analysis 10 creditsMAS333 Fields 10 creditsMAS334 Combinatorics 10 creditsMAS336 Differential Geometry 10 creditsMAS341 Graph Theory 10 creditsMAS343 History of Mathematics 10 creditsMAS344 Knots and Surfaces 10 creditsMAS345 Codes and Cryptography 10 creditsMAS346 Groups and Symmetry 10 creditsMAS348 Game Theory 10 creditsMAS360 Practical and Applied Statistics 20 creditsMAS361 Medical Statistics 10 creditsMAS362 Financial Mathematics 10 creditsMAS364 Bayesian Statistics 10 creditsMAS370 Sampling Theory and Design of Experiments 10 creditsMAS371 Applied Probability 10 creditsMAS372 Time Series 10 creditsMAS31001 Generalised Linear Models 10 credits

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(b) modules to the value of between 80 and 40 credits provided by the Department ofComputer Science as laid down in the University Regulations.

MComp Computer Science with Mathematics (COMU118) Year 3

Candidates for this degree must take

(a) modules to the value of 40 credits chosen from the following list of MAS modules:

MAS302 Undergraduate Ambassador Scheme in Mathematics 20 creditsMAS322 Operations Research 10 creditsMAS325 Mathematical Methods 10 creditsMAS330 Topics in Number Theory 10 creditsMAS331 Metric Spaces 10 creditsMAS332 Complex Analysis 10 creditsMAS333 Fields 10 creditsMAS334 Combinatorics 10 creditsMAS336 Differential Geometry 10 creditsMAS341 Graph Theory 10 creditsMAS343 History of Mathematics 10 creditsMAS344 Knots and Surfaces 10 creditsMAS345 Codes and Cryptography 10 creditsMAS346 Groups and Symmetry 10 creditsMAS348 Game Theory 10 creditsMAS360 Practical and Applied Statistics 20 creditsMAS361 Medical Statistics 10 creditsMAS362 Financial Mathematics 10 creditsMAS364 Bayesian Statistics 10 creditsMAS370 Sampling Theory and Design of Experiments 10 creditsMAS371 Applied Probability 10 creditsMAS372 Time Series 10 creditsMAS377 Mathematical Biology 10 creditsMAS442 Galois Theory 10 creditsMAS31001 Generalised Linear Models 10 credits

(b) modules to the value of 80 credits provided by the Department of Computer Science aslaid down in the University Regulations.

MComp Computer Science with Mathematics (COMU118) Year 4

Candidates for this degree must take modules to the value of 90 credits provided by theDepartment of Computer Science as laid down in the University Regulations, together withunrestricted modules to the value of 30 credits.

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BSc Economics and Mathematics (ECNU16) Year 3

Candidates for this degree must take

(a) modules to the value of 40 credits chosen from the following list of Level 3 MAS modules:

MAS302 Undergraduate Ambassador Scheme in Mathematics 20 creditsMAS322 Operations Research 10 creditsMAS330 Topics in Number Theory 10 creditsMAS331 Metric Spaces 10 creditsMAS332 Complex Analysis 10 creditsMAS333 Fields 10 creditsMAS334 Combinatorics 10 creditsMAS336 Differential Geometry 10 creditsMAS341 Graph Theory 10 creditsMAS343 History of Mathematics 10 creditsMAS344 Knots and Surfaces 10 creditsMAS345 Codes and Cryptography 10 creditsMAS346 Groups and Symmetry 10 creditsMAS348 Game Theory 10 creditsMAS350 Measure and Probability 10 creditsMAS352 Stochastic Processes and Finance 20 creditsMAS360 Practical and Applied Statistics 20 creditsMAS361 Medical Statistics 10 creditsMAS362 Financial Mathematics 10 creditsMAS364 Bayesian Statistics 10 creditsMAS31001 Generalised Linear Models 10 creditsMAS370 Sampling Theory and Design of Experiments 10 creditsMAS371 Applied Probability 10 creditsMAS372 Time Series 10 credits

(b) modules to the value of 60 or 80 credits provided by the Economics Department as laiddown in the University Regulations;

(c) unrestricted Level 3 modules to the value of up to 20 credits which may, for example, betaken from the MAS modules listed in the table above or from the Economics modulesor both. (The total number of unrestricted credits across Levels 2 and 3 combined mustnot exceed 20.)

BSc Mathematics and Philosophy (MASU25) Year 3

Candidates for this degree must take

(a) modules to the value of 50 credits chosen from the following list of Level 3 MAS modules:

MAS302 Undergraduate Ambassador Scheme in Mathematics 20 creditsMAS322 Operations Research 10 credits

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MAS330 Topics in Number Theory 10 creditsMAS331 Metric Spaces 10 creditsMAS332 Complex Analysis 10 creditsMAS333 Fields 10 creditsMAS334 Combinatorics 10 creditsMAS336 Differential Geometry 10 creditsMAS341 Graph Theory 10 creditsMAS343 History of Mathematics 10 creditsMAS344 Knots and Surfaces 10 creditsMAS345 Codes and Cryptography 10 creditsMAS346 Groups and Symmetry 10 creditsMAS348 Game Theory 10 creditsMAS350 Measure and Probability 10 credits

(b) modules to the value of 60 credits provided by the Department of Philosophy as laiddown in the University Regulations;

(c) unrestricted modules to the value of 10 credits.

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7 Cover sheet arrangements

There are some special arrangements for when assessed coursework is to be handed in atSoMaS Reception (F10).

(i) All work that needs to be submitted to Reception (F10) needs to have a cover sheet.

(ii) Students can access the cover sheet via https://sciencecoversheet.group.shef.

ac.uk/:

(a) log in with your university user name and password;

(b) cover sheets become available to students one week before the deadline to avoidearly submissions;

(c) cover sheets are unique to each student – printing out a coversheet for a frienddoesn’t work!

(iii) This then needs to be stapled (or in a plastic wallet) and then posted into the drop boxoutside reception (the drop box is provided for work that is either late/early or beingsubmitted out of office opening times).

If students have any problems with regards to viewing/accessing the cover sheets, contacthicksstudentsupport@sheffield.ac.uk or visit Reception (F10) to try and sort out theproblem.

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MAS302: Undergraduate Ambassadors SchemeSemester: Year 20 credits

Prerequisites: Agreement of module co-ordinatorCorequisites:Cannot be taken with: COM3550 (Undergraduate Ambassadors Scheme in Computer Science)Prerequisite for:

Description

MAS302 is a course which involves no formal lectures but which, instead, places students in the classroomenvironment of the Mathematics Departments of local secondary schools. The time spent within the allocatedschool is highly structured to ensure the desired outcomes of the course - see “Outcomes” and “Syllabus” inthe SoMaS database. Note that although the classroom activities take place in Semester 2, there is a selectionprocess and some training which is held in Semester 1. Further, the presentation part of the assessment willbe held in Semester 1. Students taking MAS302 might want to consider taking 70 credits in Semester 1 and50 in Semester 2 as the course is time-intensive in Semester 2.Every student who has been offered a place on the course will need to pass a DBS check (see https:

//www.gov.uk/disclosure-barring-service-check/overview). This is to ensure that you have noprevious convictions which may make you unable to work with children. These checks can be very fast, buthave taken up to 40 days.A student accepted on the course who has successfully attended the Training Day and passed the DBS checkwill not be allowed to change this module. This is due to the fact that schools spend a lot of time organisinghaving an undergraduate ambassador, and once a school has accepted a student it is important that thestudent is committed to this course.

Aims

• To develop students’ confidence in their ability to act independently in the execution of complex andimportant tasks;

• To develop the complex skills required to communicate difficult subjects in a variety of ways to peopleof widely varying abilities;

• To develop the personal skills required to engage the attention of people as individuals and of people ingroups;

• To learn the specific skills required to develop projects and teaching methods appropriate to the agegroup of pupils under tuition;

• To inspire a new generation of prospective undergraduates by providing positive role models in theclassroom;

• To stimulate pupils by conveying the excitement of their subject and showing the long-term benefits ofstudying;

• To provide additional classroom support for teachers in the form of an assistant who can work withpupils at any point on the ability spectrum;

• To provide a short, but direct, experience of teaching to those interested in pursuing it as a career.

Outline syllabus

A competitive interview system will be used to select students for the module, and to match each successfulapplicant with an appropriate school and a specific teacher in the local area. An initial day of training- held before Christmas - will provide the students with an introduction to working and conduct in theschool environment. Each student selected will be required to visit the school they will be working in beforecommencement of the unit - this visit will usually take place before Christmas. The students will be requiredto spend half a day (approximately 4 hours) each week in the school for ten weeks of the second semester.It is intended that there will be no formal lectures associated with the unit, and that wherever appropriatethe students’ own ideas will increasingly define the nature of their teaching activities as they become moreexperienced. However, there will be supporting tutorials which will provide an opportunity for students toshare their experiences with their contempories and the module coordinators. The teachers will act as themain source of guidance but, in addition, students will be able to discuss their progress with the modulecoordinators whenever necessary.

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Assessment

A weekly diary [10%]; End-of-module written report [35%]; A written account of your special project [20%]; Afifteen minute oral presentation [20%]; Assessment by the teacher moderated by module coordinator [7.5%];Overall impression of the portfolio [7.5%].

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MAS322: Operations ResearchSemester: 2 10 credits

Prerequisites: MAS211 (Advanced Calculus and Linear Algebra)Corequisites:Cannot be taken with: MAS423 (Advanced Operations Research)Prerequisite for:

Description

Mathematical Programming is the title given to a collection of optimisation algorithms that deal with con-strained optimisation problems. In this module the problems considered will mostly involve constraints whichare linear, and for which the objective function to be maximised or minimised is also linear. Some of theseproblems are not continuously differentiable; special algorithms have to be developed. The module considersfirst how these problems arise from practical applications, then introduces the methods to find and analysethe solutions, and concludes with a brief introduction of the dual problems.

Aims

• To develop the mathematical skills that will provide you with the appropriate foundations for furthermathematical studies.

• To enable you to analyse OR problems that may arise in your future employment.

Outline syllabus

• Building linear programming, integer programming and piecewise linear programming models• Graphical techniques• The Simplex Method and variants• Matrix representation of the simplex algorithm• Elementary post-optimality analysis• Duality

Module Format

Lectures 20 Tutorials 1 Practicals 0

Recommended books

B Paul R. Thie and Gerard E. Keough “An Introduction to Linear Programming and Game Theory”(Shelfmark 518.7 (T), ISBN 978-0470232866)

B Taha “Operations Research” (Shelfmark 519.38 (T), ISBN 0131889230)

C Bertsimas and Tsitsiklis “Introduction to Linear Optimization.” (Shelfmark 519.72 (B), ISBN 1886529191)

C Winston “Introduction to Mathematical Programming” (Shelfmark 519.7 (W), ISBN 0534359647)

Assessment

One formal 2 hour written examination with 4 compulsory questions [75%]. Mini-project [25%].

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MAS325: Mathematical MethodsSemester: 2 10 credits

Prerequisites: MAS211 (Advanced Calculus and Linear Algebra)Corequisites:Cannot be taken with:Prerequisite for:

Description

This course introduces methods which are useful in many areas of mathematics. The emphasis will mainlybe on obtaining approximate solutions to problems which involve a small parameter and cannot easily besolved exactly. These problems will include the evaluation of integrals. Examples of possible applications are:oscillating motions with small nonlinear damping, the effect of other planets on the Earth’s orbit around theSun, boundary layers in fluid flows, electrical capacitance of long thin bodies, central limit theorem correctionterms for finite sample size.

Aims

• To develop methods for solving differential equations using integral transforms and representations.• To introduce asymptotic methods for solving algebraic equations.• To introduce asymptotic methods for evaluating integrals.

Outline syllabus

• Integral methods and differential equations: Dirac δ-function, Fourier and Laplace transforms, applica-tions to differential equations, Green functions.

• Asymptotic expansions: algebraic equations with small parameter, asymptotic expansion of functionsdefined by integrals.

Module Format

Lectures 20 Tutorials 0 Practicals 0

Recommended books

C Barndorff-Nielsen and Cox “Asymptotic Techniques for Use in Statistics” (Shelfmark 519.5 (B), ISBN0412314002)

C Bender and Orszag “Advanced Mathematical Methods for Scientists and Engineers I: Asymptotic Meth-ods and Perturbation Theory” (Shelfmark 515.350245 (B), ISBN 0387989315)

C Copson “Asymptotic Expansions” (Shelfmark 3 PER 510.5/CAM, ISBN 0521604826)

C Hinch “Perturbation Methods” (Shelfmark 517.9 (H), ISBN 0521373107)

C Jordan and Smith “Mathematical Techniques” (Shelfmark 510 (J), ISBN 0199249725)

C Kevorkian and Cole “Multiple Scale and Singular Perturbation Methods” (Shelfmark 517.9 (K), ISBN0387942025)

C King, Billingham and Otto “Differential Equations” (Shelfmark 515.35 (K), ISBN 0521816580)

C Lin and Segel “Mathematics Applied to Deterministic Problems in the Natural Sciences” (Shelfmark510 (L), ISBN 0898712297)

C Olver “Asymptotics and Special Functions” (Shelfmark 517.5217 (O), ISBN 1568810695)

C Van Dyke “Perturbation Methods in Fluid Mechanics” (Shelfmark 532 (V), ISBN 0915760010)

Assessment

One formal 2 hour written examination. Format: 4 questions from 5.

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MAS330: Topics in Number TheorySemester: 1 10 credits

Prerequisites: MAS211 (Advanced Calculus and Linear Algebra)Corequisites:Cannot be taken with:Prerequisite for: Desirable for MAS345 (Codes and Cryptography)

Description

The course covers topics in elementary Number Theory. This includes Modular Arithmetic, and properties ofprimes and integers. Most of the material (with the notable exception of the RSA cryptosystem) has beenintroduced by Fermat, Euler and Gauss in the 17th, 18th and 19th centuries.

Aims

• To introduce various topics in number theory

Outline syllabus

1. Modular Arithmetic

• Linear Congruences

• Fermat’s Little Theorem and the RSA cryptosystem.

• Arithmetic functions.

• Euler’s function and Euler’s theorem.

• Gauss’ Quadratic Reciprocity Law.

2. Primes, Integers and Equations

• Perfect numbers, Mersenne primes, Fermat primes.

• Pythagorean triples and Fermat Last Theorem.

• Fibonacci numbers.

• Continued fractions.

• Pell’s equation.

Module Format

Lectures 20 Tutorials 0 Practicals 0

Recommended books

B Burton “Elementary Number Theory” (Shelfmark 512.81 (B), ISBN 0071121749)

C Singh “Fermat’s Last Theorem” (Shelfmark 511.52(S), ISBN 000724181X)

Assessment

One formal 2.5 hour written examination. Format: 4 questions from 4.

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MAS331: Metric SpacesSemester: 1 10 credits

Prerequisites: MAS221 (Analysis)Corequisites:Cannot be taken with:Prerequisite for: MAS435 (Algebraic Topology); MAS436 (Functional Analysis)

Description

This unit explores ideas of convergence of iterative processes in the more general framework of metric spaces.A metric space is a set with a “distance function” which is governed by just three simple rules, from which theentire analysis follows. The course follows on from MAS221 Analysis, and adapts some of the ideas from thatcourse to the more general setting. The course ends with the Contraction Mapping Theorem, which guaranteesthe convergence of quite general processes; there are applications to many other areas of mathematics, suchas to the solubility of differential equations.

Aims

• To point out that iterative processes and convergence of sequences occur in many areas of mathematics,and to develop a general context in which to study these processes

• To provide a basic course in analysis in this setting• To reinforce ideas of proof• To illustrate the power of abstraction and show why it is worthwhile• To provide a foundation for later analysis courses

Outline syllabus

• Examples of iterative processes in various settings• Metric spaces: definition, properties and examples• Convergence of sequences• Closed subsets, continuity• Cauchy sequences, completeness, compactness• The Contraction Mapping Theorem

Module Format

Lectures 20 Tutorials 0 Practicals 0

Recommended books

B Bryant “Metric Spaces: Iteration and Application” (Shelfmark 512.811 (B), ISBN 0521268575)

B Carothers “Real Analysis” (Shelfmark 517.51 (C), ISBN 0521497493)

B Haaser and Sullivan “Real Analysis” (Shelfmark 517.51(H), ISBN 0486665097)

C Kreyszig “Introductory Functional Analysis with Applications” (Shelfmark 517.5 (S), ISBN 0471507318)

Assessment

One formal 2.5 hour written examination. Format: 4 compulsory questions.

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MAS332: Complex AnalysisSemester: 1 10 credits

Prerequisites: MAS211 (Advanced Calculus and Linear Algebra)Corequisites:Cannot be taken with:Prerequisite for: MAS430 (Analytic Number Theory); MAS436 (Functional Analysis)

Description

It is natural to use complex numbers in algebra, since these are the numbers we need to provide the roots of allpolynomials. In fact, it is equally natural to use complex numbers in analysis, and this course introduces thestudy of complex-valued functions of a complex variable. Complex analysis is a central area of mathematics.It is both widely applicable and very beautiful, with a strong geometrical flavour. This course will considersome of the key theorems in the subject, weaving together complex derivatives and complex line integrals.There will be a strong emphasis on applications.

Aims

• To introduce complex functions of a complex variable• To demonstrate the critical importance of differentiability of complex functions of a complex variable,

and its surprising relation with path-independence of line integrals• To demonstrate the relevance of power series in complex analysis• To develop the subject of complex analysis rigorously, highlighting its logical structure and proving several

of the fundamental theorems• To discuss some applications of the theory, including to the calculation of real integrals

Outline syllabus

• Revision of complex numbers• Special functions• Simple integrals of complex-valued functions• Open sets, neighbourhoods and regions• Differentiability; Cauchy-Riemann equations, harmonic functions• Power series and special functions• Complex line integrals• Cauchy’s Theorem• Cauchy’s integral formula and Cauchy’s formula for derivatives• Liouville’s Theorem• The Fundamental Theorem of Algebra• Taylor’s Theorem• Laurent’s Theorem and singularities• Cauchy’s Residue Theorem and applications

Module Format

Lectures 20 Tutorials 0 Practicals 0

Recommended books

B Priestley “Introduction to Complex Analysis” (Shelfmark 517.53 (P), ISBN 0198534299)

B Stewart and Tall “Complex Analysis” (Shelfmark 517.53 (S), ISBN 0521245133)

B Wunsch “Complex Variables with Applications” (ISBN 0201122995)

C Spiegel “Complex Variables” (Shelfmark 517.53 (S), ISBN 0070843821)

Assessment

One formal 2.5 hour written examination. Format: 4 questions from 5.

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MAS333: FieldsSemester: 1 10 credits

Prerequisites: MAS220 (Algebra)Corequisites:Cannot be taken with: MAS438 (Fields)Prerequisite for: Either this module or MAS438 (Fields) is needed for MAS442 (Galois Theory)

Description

A field is a set where the familiar operations of arithmetic are possible. It often happens, particularly in thetheory of equations, that one needs to extend a field by forming a bigger one. The aim of this course isto study the idea of field extension and various problems where it arises. In particular, it is used to answersome classical problems of Greek geometry, asking whether certain geometrical constructions, such as angletrisection or squaring the circle, are possible.

Aims

• To illustrate how questions concerning the complex roots of real or rational polynomial equations canquickly lead to the study of subfields of the field of complex numbers

• To consolidate previous knowledge of field theory and vector space theory• To illustrate how the general mathematical theory of vector spaces can be used to good effect in the

theory of field extensions• To illustrate how the theory of dimensions of vector spaces can be used to prove that certain ruler and

compass constructions are impossible• To illustrate the relevance of factorization of polynomials to the theory of algebraic field extensions

Outline syllabus

• Field extensions• Factorization of polynomials• Simple field extensions• Towers of fields• Ruler and compass constructions

Module Format

Lectures 20 Tutorials 0 Practicals 0

Recommended books

B Allenby “Rings, Fields and Groups” (Shelfmark 512.8 (A), ISBN 0340544406)

B Fraleigh “A First Course in Abstract Algebra” (Shelfmark 512.8 (F), ISBN 0201534673)

B Herstein “Abstract Algebra” (Shelfmark 512.8 (H), ISBN 0023538228)

B Stewart “Galois Theory” (Shelfmark 512.43 (S), ISBN 0412345404)

Assessment

One formal 2.5 hour written examination. Format: 4 questions from 4.

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MAS334: CombinatoricsSemester: 1 10 credits

Prerequisites: MAS211 (Advanced Calculus and Linear Algebra)Corequisites:Cannot be taken with:Prerequisite for:

Description

Combinatorics is the mathematics of selections and combinations. For example, given a collection of sets,when is it possible to choose a different element from each of them? That simple question leads to Hall’sTheorem, a far-reaching result with applications to counting and pairing problems throughout mathematics.

Aims

• To illustrate the wide range of selection problems in combinatorial mathematics• To teach the basic techniques of selection and arrangement problems• To show how to solve a wide range of natural counting problems using these techniques

Outline syllabus

• The binomial coefficients• Three basic principles: parity, pigeon-holes and inclusion/exclusion• Rook polynomials• Hall’s Marriage Theorem and its applications• Latin squares• Block designs and codes

Module Format

Lectures 20 Tutorials 0 Practicals 0

Recommended books

B Anderson “A First Course in Combinatorial Mathematics” (Shelfmark 519.21 (A), ISBN 0198596731)

B Bryant “Aspects of Combinatorics” (Shelfmark 519.21 (B), ISBN 0521429978)

Assessment

One formal 2.5 hour examination. Format: answer all questions.

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MAS336: Differential GeometrySemester: 1 10 credits

Prerequisites: MAS211 (Advanced Calculus and Linear Algebra)Corequisites:Cannot be taken with:Prerequisite for:

Description

Differential geometry is the study of geometric objects using calculus, and it has plenty of applications in othersciences and engineering. In this introductory course, the geometric objects of our interest will be curves andsurfaces. You will learn more about such familiar notions as arc lengths, angles and areas. You will also learnhow to quantify the “shape” of an object, via various notions of curvature. There are rich interactions betweencurvature and other geometric quantities, as illustrated most notably by Gauss’ Theorem. For example, wecan make a map of the Earth that correctly represents either all angles or all areas; but by Gauss’ Theorem,the Earth’s curvature prevents us from ever making a map that correctly represents distances.

Aims

• to introduce differential geometry: its goals, techniques and applications;• to translate intuitive ideas into mathematical concepts that allow quantitative studies and development

of sophisticated results;• to illustrate geometric concepts and results through many examples.

Outline syllabus

Curves in R2

• Basic notions and examples• Curvature

Surfaces in R3

• Basic notions and examples• Metric quantities• Curvature• Gauss’ Theorem

Module Format

Lectures 20 Tutorials 0 Practicals 0

Recommended books

B Pressley “Elementary Differential Geometry” (Shelfmark 513.73 (P), ISBN 9781848828902)

Assessment

One formal 2.5 hour written examination. Format: 4 questions from 4.

40

MAS341: Graph TheorySemester: 2 10 credits

Prerequisites: MAS211 (Advanced Calculus and Linear Algebra)Corequisites:Cannot be taken with:Prerequisite for:

Description

A “graph” is a simple mathematical structure consisting of a collection of points, some pairs of which arejoined by lines. Their basic nature means that they can be used to illustrate a wide range of situations. Theaim of this course is to investigate the mathematics of these structures and to use them in a wide range ofapplications. Topics covered include trees, Eulerian and Hamiltonian graphs, planar graphs, embedding ofgraphs in surfaces, and graph colouring.

Aims

• To expound the theory of graphs with brief consideration of some algorithms

Outline syllabus

• Definition and examples• Trees• Eulerian graphs• Hamiltonian graphs• The Travelling Salesman Problem• The Shortest and Longest Path Algorithms• Planar graphs• Embedding graphs in surfaces• Vertex colouring• Edge colouring• Face colouring

Module Format

Lectures 20 Tutorials 0 Practicals 0

Recommended books

B Bryant “Aspects of Combinatorics” (Shelfmark 519.21 (B), ISBN 0521429978)

B Wilson “Introduction to Graph Theory” (Shelfmark 513.83 (W), ISBN 0582249937)

C Wilson “Four Colours Suffice” (Shelfmark 513.83 (W), ISBN 014100908x)

Assessment

One formal 2.5 hour written examination. Format: 4 questions from 4.

41

MAS343: History of MathematicsSemester: 2 10 credits

Prerequisites:Corequisites:Cannot be taken with:Prerequisite for:

Note: the following information should be considered indicative of the module contents rather than beingfinalised. The precise syllabus will be dependent on the expertise of the module lecturer. The actual syllabuswill be available before the start of the module.

Description

The course aims to introduce the student to the study of the history of mathematics. The main topicsdiscussed are Egyptian and Babylonian mathematics, early Greek mathematics, Renaissance mathematics, andthe early history of the calculus.

Aims

• To introduce the student to the history of mathematics• To place mathematical developments into historical perspective• To train the student to study from a set text• To encourage independent study and use of the University’s libraries• To allow students to research a topic and then write up a formal report or produce a poster on their

findings, which counts towards the continuous assessment part of the course• To discuss developments in mathematics in various periods, including its beginnings in the Egyptian

and Mesopotamian civilizations, its flowering under the ancient Greeks and its renaissance in sixteenth-century Europe.

• To trace the pre-history of the calculus from its beginnings in Greece to its rapid expansion in seventeenth-century Europe.

Outline syllabus

• Introduction• Egypt and Mesopotamia• Early Greek mathematics• Renaissance mathematics• The route to the calculus

Module Format

Lectures 20 Tutorials 0 Practicals 0

Recommended books

A Boyer and Merzbach “A History of Mathematics” (Shelfmark 510.9 (B), ISBN 0471543977)

B Katz “A History of Mathematics” (Shelfmark 510.9 (K), ISBN 0321016181)

C Fauvel and Gray “The History of Mathematics: A Reader” (Shelfmark 510.9 (H), ISBN 0333427912)

Assessment

One formal 2.5 hour written examination [69%]. Format: 1 compulsory question plus 3 questions from 4.Coursework [31%].

42

MAS344: Knots and SurfacesSemester: 2 10 credits

Prerequisites: MAS114 (Numbers and Groups)Corequisites:Cannot be taken with:Prerequisite for:

Description

The course studies knots, links and surfaces in an elementary way. The key mathematical idea is that of analgebraic invariant: the Jones polynomial for knots, and the Euler characteristic for surfaces. These invariantswill be used to classify surfaces, and to give a practical way to place a surface in the classification. Variousconnections with other sciences will be described.

Aims

• To present a classification, that of compact surfaces, beginning from definitions and basic examples• To instill an intuitive understanding of knots and compact surfaces• To introduce and illustrate discrete invariants of geometric problems• To show that adding extraneous structure may give information independent of that structure• To develop the theory of the Euler characteristic• To illustrate how a general mathematical theory can apply to quite different physical objects, and solve

very specific problems about them

Outline syllabus

• Knots and links• The Jones polynomial• Surfaces• The Euler characteristic

Module Format

Lectures 20 Tutorials 0 Practicals 0

Recommended books

B Firby and Gardiner “Surface Topology” (Shelfmark 513.83 (F), ISBN 1898563772)

C Adams “The Knot Book” (Shelfmark 513.83 (A), ISBN 0821836781)

C Cundy and Rollett “Mathematical Models” (Shelfmark 510.84 (C), ISBN 0906212200)

C Gilbert and Porter “Knots and Surfaces” (Shelfmark 513.83 (G), ISBN 0198514905)

C Kauffman “On Knots” (Shelfmark 513.83 (K), ISBN 0691084351)

Assessment

One formal 2.5 hour written examination. Format: 4 compulsory questions.

43

MAS345: Codes and CryptographySemester: 2 10 credits

Prerequisites: MAS220 (Algebra);MAS330 (Topics in Number Theory) desirable

Corequisites:Cannot be taken with:Prerequisite for:

Description

The word ‘code’ is used in two different ways. The ISBN code of a book is designed in such a way that simpleerrors in recording it will not produce the ISBN of a different book. This is an example of an ‘error-correctingcode’ (more accurately, an error-detecting code). On the other hand, we speak of codes which encryptinformation — a topic of vital importance to the transmission of sensitive financial information across theinternet. These two ideas, here labelled ‘Codes’ and ‘Cryptography’, each depend on elegant pure mathematicalideas: codes on linear algebra and cryptography on number theory. This course explores these topics, includingthe real-life applications and the mathematics behind them.

Aims

• To introduce the basic ideas connected with error detection and error correction, and various examplesof useful codes

• To demonstrate the importance of the simple concepts of Hamming distance and the minimum distanceof a code in the theory of error detection and error correction

• To illustrate how linear algebra can be used to good effect in the theory of linear codes• To give an overview of cryptography from the most basic examples to modern public key systems• To introduce the number-theoretic concepts used in public-key cryptosystems and to show how these

are applied in practical examples

Outline syllabus

• Codes and linear codes• Hamming distance• Examples of error-correcting/error-detecting codes• Classical methods of cryptography• Results from number theory• Public key methods of cryptography

Module Format

Lectures 20 Tutorials 0 Practicals 0

Recommended books

C Hill “A First Course in Coding Theory” (Shelfmark 003.54 (H), ISBN 0198538030)

C Koblitz “A Course in Number Theory and Cryptography” (Shelfmark 512.81 (K), ISBN 0387942939)

C Singh “The Code Book” (ISBN 1857028899)

C Welsh “Codes and Cryptography” (Shelfmark 003.54 (W), ISBN 0198532873)

C Young “Mathematical Ciphers: from Caesar to RSA” (ISBN 0821837303)

Assessment

One formal 2.5 hour written examination. Format: 4 compulsory questions, two on Codes and two onCryptography.

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MAS346: Groups and SymmetrySemester: 2 10 credits

Prerequisites: MAS211 (Advanced Calculus and Linear Algebra); MAS220 (Algebra)Corequisites:Cannot be taken with:Prerequisite for:

Description

Groups arise naturally as collections of symmetries. Examples considered include symmetry groups of Platonicsolids and of wallpaper patterns. Groups can also act as symmetries of other groups. These actions can beused to prove the Sylow theorems, which give important information about the subgroups of a given finitegroup, leading to a classification of groups of small order.

Aims

• To consolidate previous knowledge of group theory, symmetries and linear algebra• To display and exemplify the ubiquity of groups as symmetries of physical and mathematical objects• To introduce and illustrate the process of analysis of a finite group from its local structure

Outline syllabus

• Orthogonal and special orthogonal symmetries of Rn

• Group actions, Sylow theorems, and simple groups• Symmetry and direct symmetry groups• Affine isometries• Wallpaper groups• Groups of symmetries of the platonic solids• Groups of small order

Module Format

Lectures 20 Tutorials 0 Practicals 0

Recommended books

B Armstrong “Groups and Symmetry” (Shelfmark 512.86 (A), ISBN 0387966757)

B Dummit “Abstract Algebra” (Shelfmark 512.8 (D), ISBN 0130047716)

B Fraleigh “A First Course in Abstract Algebra” (Shelfmark 512.8 (F), ISBN 0201534673)

B Herstein “Abstract Algebra” (Shelfmark 512.8 (H), ISBN 0023538228)

C Artin “Algebra” (Shelfmark 512 (A), ISBN 0130047635)

Assessment

One formal 2.5 hour written examination.

45

MAS348: Game TheorySemester: 1 10 credits

Prerequisites: MAS113 (Introduction to Probability and Statistics) recommended;MAS211 (Advanced Calculus and Linear Algebra)

Corequisites:Cannot be taken with: ECN306 (Game Theory for Economists)Prerequisite for:

Description

The module will give students an opportunity to apply previously acquired mathematical skills to the study ofGame Theory and to some of its applications in Economics.

Aims

• To understand the mathematical concept of a game and to see its manifestations in various real-lifesettings.

• To understand the notion of Nash equilibrium.

• To understand the technique of backward induction and its applications in the context of sequentialgames.

• To understand the notion of subgame-perfect Nash equilibria in sequential games.

• To understand the complexities of repeated games.

• To understand the concept of a Bayesian Game and their Nash equilibria.

Outline syllabus

• The formal definition of games both in strategic for and in sequential form.

• Dominated strategies and the solution of games by iterative elimination of dominated strategies.

• Pure and mixed Nash equilibria of games.

• Sequential games: backward induction, Zermelo’s Theorem, subgame perfect Nash equilibria and im-perfect information.

• Translation of games in normal form to sequential form and viceversa.

• Applications of game theoretical techniques to real-life problems, e.g., in Economics.

• The notion of equilibria of repeated games.

• Bayesian games and their equilibria.

Module Format

Lectures 20 Tutorials 0 Practicals 0

Recommended books

B K.G. Binmore “Playing for Real: a Text on Game Theory” (Shelfmark 519.3 (B), ISBN 978-0195300574)

B M.J. Osborne “An Introduction to Game Theory” (Shelfmark 519.3(O), ISBN 9780195322484)

Assessment

One 2.5 hour exam.

46

MAS350: Measure and ProbabilitySemester: 2 10 credits

Prerequisites: MAS211 (Advanced Calculus and Linear Algebra); MAS221 (Analysis)Corequisites:Cannot be taken with: MAS451 (Measure and Probability)Prerequisite for:

Description

Measure theory is that branch of mathematics which evolves from the idea of “weighing” a set by attachinga non-negative number to it which signifies its worth. This generalises the usual physical ideas of length,area and mass as well as probability. It turns out (as we will see in the course) that these ideas are vital fordeveloping the modern theory of integration.The module will give students an additional opportunity to develop skills in modern analysis as well as providinga rigorous foundation for probability theory. In particular it would form a useful precursor or companion courseto the Level 4 courses MAS436 (Functional Analysis) and MAS452 (Stochastic Processes and Finance), thelatter of which is fundamentally dependent on measure theoretic ideas.

Aims

• Give a more rigorous introduction to the theory of measure.• Develop the ideas of Lebesgue integration and its properties.• Recall the concepts of probability theory and consider them from a measure theoretic point of view.• Prove the Central Limit Theorem using these methods.

Outline syllabus

• The scope of measure theory,• σ-algebras,• Properties of measures,• Measurable functions,• The Lebesgue integral,• Interchange of limit and integral,• Probability from a measure theoretic viewpoint,• Characteristic functions,• The central limit theorem.

Module Format

Lectures 20 Tutorials 0 Practicals 0

Recommended books

C Williams “Probability With Martingales” (Shelfmark 519.236 (W), ISBN 0 521 40605 6 )

C Cohn “Measure Theory” (Shelfmark 3B 517.29 (C), ISBN 0-8176-3003-1)

C Rosenthal “A First Look at Rigorous Probability ” (Shelfmark 519.2 (R), ISBN 081-02-4303-0)

Assessment

One 2.5 hour exam.

47

MAS352: Stochastic Processes and FinanceSemester: Year 20 credits

Prerequisites: MAS113 (Introduction to Probability and Statistics);MAS221 (Analysis);MAS275 (Probability Modelling);MAS223 (Statistical Inference and Modelling) recommended

Corequisites:Cannot be taken with: MAS452 (Stochastic Processes and Finance)Prerequisite for:

Description

A stochastic process is a mathematical model for a randomly evolving system. In this course we study severalexamples of stochastic process and analyse their behaviour. We apply our knowledge of stochastic processesto mathematical finance, in particular to asset pricing and the Black-Scholes model.

Aims

• Introduce probability spaces, σ-fields and conditional expectation.• Introduce martingales and study their basic properties.• Analyse the behaviour of different types of stochastic process, such as random walks, urn models and

branching processes.• Explain the role of arbitrage and arbitrage free pricing.• Use finite market models to price and hedge a range of financial derivatives.• Introduce Brownian motion and study its basic properties.• Introduce stochastic calculus, Ito’s formula and stochastic differential equations.• Derive the Black-Scholes formula in continuous time and use it to price a range of financial derivatives.• Study extensions of the Black-Scholes formula.

Outline syllabus

• Stochastic Processes: We introduce conditional expectation and martingales, which are used to studythe behaviour of stochastic processes such as random walks, urn models, branching processes, Brownianmotion and diffusions. Stochastic integration with respect to Brownian motion is introduced.

• Stochastic Finance: We study the key concept of arbitrage and arbitrage free pricing, both in finitemarkets and in the continuous time Black-Scholes model.

Module Format

Lectures 40 Tutorials 0 Practicals 0

Recommended books

C A Etheridge “A Course in Financial Calculus” (Shelfmark 332.0151922 (E), ISBN 0521890772)

C T Bjork “Arbitrage Theory in Continuous Time” (ISBN 9780199271269)

C P Wilmott, S Howison, J Dewynne “The Mathematics of Financial Derivatives” (Shelfmark 332.64 (W),ISBN 0521496993)

C D Williams “Probability with Martingales” (Shelfmark 519.236 (W), ISBN 0521406056)

Assessment

One formal 3 hour written closed book examination.

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MAS360: Practical and Applied StatisticsSemester: Year 20 credits

Prerequisites: MAS223 (Statistical Inference and Modelling)Corequisites: MAS367 (Linear and Generalised Linear models) recommendedCannot be taken with: MAS301 (Group Project)Prerequisite for:

Description

This course aims to give you practice in solving problems of the sort you will encounter in real life as aprofessional mathematician or statistician. It gives training and practice in the various stages: problem defini-tion, preliminary examination of data, modelling, analysis, computation, interpretation and communication ofresults. It is comprised of a series of exercises (not assessed) and projects (assessed).Teaching is directed towards skills development. Use of R for linear modelling is revised; specific guidanceis given regarding presentation skills (oral and written) and group working; but no new technical materialis taught. Instead, you are encouraged to recall and collate the technical material gained over the entireremainder of your degree programme and to identify and implement those methods which are appropriateand useful in addressing the problem at hand. This vital skill, of synthesizing and evaluating your existingknowledge, allows you to show yourself at your best in examinations, interviews and the early days of a futurecareer.

Aims

• To develop students’ skills in open-ended tasks with a substantial statistical aspect.• To develop students’ abilities to report on the results of their investigations.

Outline syllabus

There is no technical syllabus for this course; indeed it is deliberately arranged that no new theory is needed,although students may need to use extended versions of familiar topics or invent ad hoc methods. Instructionis given in writing reports and in tackling imprecisely worded or open-ended problems. Feedback on projectsattempted continues this instruction.

Module Format

Lectures 30 Tutorials 0 Practicals 0

Recommended books

• There are no recommended books for this course.

Assessment

Entirely continuous assessment, through project reports and presentations. The weighting and deadlines willbe announced during the module.

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MAS361: Medical StatisticsSemester: 1 10 credits

Prerequisites: MAS223 (Statistical Inference and Modelling)Corequisites:Cannot be taken with: MAS61002 (Medical Statistics)Prerequisite for:

Description

This course comprises sections on Clinical Trials and Survival Data Analysis. The special ethical and regulatoryconstraints involved in experimentation on human subjects mean that Clinical Trials have developed theirown distinct methodology. Students will, however, recognise many fundamentals from mainstream statisticaltheory. The course aims to discuss the ethical issues involved and to introduce the specialist methods required.Prediction of survival times or comparisons of survival patterns between different treatments are examples ofparamount importance in medical statistics. The aim of this course is to provide a flavour of the statisticalmethodology developed specifically for such problems, especially with regard to the handling of censored data(e.g., patients still alive at the close of the study). Demonstrating implementation of the statistical analysesin the R package is an important part of the course.

Aims• To illustrate applications of statistics within the medical field.• To introduce students to some of the distinctive statistical methodologies developed to tackle problems

specifically related to clinical trials and the analysis of survival data.

Outline syllabus• Clinical Trials:

– Basic concepts and designs: controlled and uncontrolled clinical trials; historical controls; pro-tocol; placebo; randomisation; blind and double blind trials; ethical issues; protocol deviations.

– Size of trials.– Multiplicity and meta-analysis: interim analyses; multi-centre trials; combining trials.– Cross-over trials.– Binary response data: logistic regression modelling; McNemar’s test, relative risks, odds ratios.

• Survival Data Analysis:

– Basic concepts: survivor function; hazard function; censoring.– Single sample methods: lifetables; Kaplan-Meier survival curve; parametric models.– Two sample methods: log-rank test; parametric comparisons.– Regression models: inclusion of covariates; Cox’s proportional hazards model.

Module Format

Lectures 18 Tutorials 2 Practicals 0

Recommended books

A Everitt and Rabe-Heskith “Analyzing Medical Data Using S-Plus” (Shelfmark 610.285 (E))

A Matthews “An Introduction to Randomized Controlled Clinical Trials” (Shelfmark 615.50724)

B Altman “Practical Statistics for Medical Research” (Shelfmark 519.023 (A), ISBN 1584880392)

B Campbell “Statistics at Square Two” (Shelfmark 519.023 (C), ISBN 1405134909)

B Collett “Modelling Survival Data in Medical Research” (Shelfmark 610.727 (C), ISBN 1584883251)

Assessment

One formal 2 hour written examination. Format: 3 questions from 4.

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MAS362: Financial MathematicsSemester: 1 10 credits

Prerequisites: MAS223 (Statistical Inference and Modelling); MAS221 (Analysis) recommendedCorequisites:Cannot be taken with: MAS462 (Financial Mathematics)Prerequisite for:

Description

The discovery of the Capital Asset Pricing Model by William Sharpe in the 1960’s and the Black-Scholesoption pricing formula a decade later mark the beginning of a very fruitful interaction between mathematicsand finance. The latter obtained new powerful analytical tools while the former saw its knowledge applied innew and surprising ways. (A key result used in the derivation of the Black-Scholes formula, Ito’s Lemma, wasfirst applied to guide missiles to their targets; hence the title ‘rocket science’ applied to financial mathematics).This course describes the mathematical ideas behind these developments together with their applications inmodern finance.

Aims

• To introduce students to the mathematical ideas and methods used in finance.• To familiarise students with financial instruments such as shares, bonds, forward contracts, futures and

options.• To familiarise students with the notion of arbitrage and the notion of no-arbitrage pricing.• To introduce the binomial tree and geometric Brownian motion models for stock prices.• To familiarise students with the Black-Scholes option pricing method.• To introduce the Capital Asset Pricing Model.

Outline syllabus

• Introduction, arbitrage, forward and futures contracts• Options, binomial trees, risk-neutral valuation• Brownian motion and share prices, the Black-Scholes analysis• Portfolio theory, the Capital Asset Pricing Model

Module Format

Lectures 20 Tutorials 0 Practicals 0

Recommended books

B Capinski and Zastawniak “Mathematics for Finance: An Introduction to Financial Engineering” (Shelf-mark 332.0151 (C), ISBN 1852333308)

B Hull “Options, Futures and Other Derivatives” (Shelfmark 332.645 (H), ISBN 0131499084)

B Sharpe “Portfolio Theory and Capital Markets” (Shelfmark 332.6 (S), ISBN 0071353208)

Assessment

One formal 2.5 hour written examination. Format: 4 questions from 4.

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MAS364: Bayesian StatisticsSemester: 1 10 credits

Prerequisites: MAS223 (Statistical Inference and Modelling)Corequisites:Cannot be taken with: MAS464 (Bayesian Statistics)Prerequisite for: Either this module or MAS464 (Bayesian Statistics) is needed for MAS472 (Com-

putational Inference)

Description

This unit develops the Bayesian approach to statistical inference. The Bayesian method is fundamentally differ-ent in philosophy from conventional frequentist/classical inference and is increasingly popular in many fields ofapplied statistics. This course will cover both the foundations of Bayesian statistics, including subjective prob-ability, utility and decision theory, and modern computational tools for practical inference problems, specificallyMarkov Chain Monte Carlo methods and Gibbs sampling. Applied Bayesian methods will be demonstrated ina series of case studies using the programming language R.

Aims

• To extend understanding of the practice of statistical inference.• To familiarize the student with the Bayesian approach to inference.• To describe computational implementation of Bayesian analyses.

Outline syllabus

• Subjective probability.• Inference using Bayes’ Theorem. Prior distributions. Exponential families. Conjugacy. Exchangeability.• Predictive inference.• Utility and decisions. Point and interval estimation from a decision-theoretic perspective.• Hierarchical models.• Computation. Gibbs sampling. Metropolis-Hastings. Case studies.• Linear regression.

Module Format

Lectures 20 Tutorials 0 Practicals 3

Recommended books

B Gelman, Carlin, Stern and Rubin “Bayesian Data Analysis” (Shelfmark 519.42 (W), ISBN 0412039915)

B Lee “Bayesian Statistics: An Introduction” (Shelfmark 519.542 (L), ISBN 0340814055)

Assessment

One formal 2 hour written examination [85%]. Format: 3 questions from 4. Continuous assessment [15%];three assignments, each worth 5%.

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MAS31001: Generalised Linear ModelsSemester 2 10 credits

Prerequisites: MAS223 (Statistical Inference and Modelling)Corequisites:Cannot be taken with:Prerequisite for:

Description

This module introduces the theory and application of generalised linear models (GLMs). Such models canbe used for modelling binary or count data, where the dependent variable is not normally distributed; thisincreases the range of problems that can be studied substantially. The general theory will be presented, inwhich the ordinary linear model is a special case. Application of the methods will be demonstrated using R,including the use of exploratory data analysis methods as a precursor to modelling.

Aims

• To introduce the theory of generalised linear models.• To show how these methods are applied to data, and what kinds of conclusions are possible.• To demonstrate how generalised linear models can be fitted to data using R.

Outline syllabus

• Revision of the normal theory linear model, focusing on the linear predictor and the assumptions.• Exploratory data analysis: understanding the data before fitting a GLM• Introduction to GLMs: motivation with some examples, link functions, GLM dis- tributions and assump-

tions, distributional properties.• Fitting GLMs: the likelihood, implementation in R• Model fit and variable selection: deviance, Pearson X2, comparing nested models, residuals, estimation

of dispersion parameter.• Binomial regression: link functions, model building, odds ratios, examples.• Poisson regression: modelling of counts, offsets, examples.• Over-dispersion: quasi-likelihood, quasibinomial, quasi-Poisson.• Contingency tables as Poisson regression• Penalised likelihood and AIC for both GLMs and normal theory linear models; step- wise selection.• Ordinal and multinomial logistic regression• Mixed effects modelling within GLMs.

Module Format

Lectures 20 Tutorials 0 Practicals 0

Recommended books

C Dobson, A.J. and Adrian Barnett “An Introduction to Generalized Linear Models”

C McCullagh, P J and Nelder, J A “Generalised Linear Models” (ISBN 0471315656)

Assessment

One formal 2 hour examination [100%].

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MAS369: Machine LearningSemester: 1 10 credits

Prerequisites: MAS223 (Statistical Inference and Modelling)Corequisites:Cannot be taken with:Prerequisite for:

Description

Machine learning lies at the interface between computer science and statistics. The aims of machine learningare to develop a set of tools for modelling and understanding complex data sets. Tools of statistical machinelearning have become important in many fields, such as marketing, finance and business, as well as in science.The module focuses on the problem of training models to learn from existing data to classify new examplesof data. Although other aspects of machine learning will be mentioned, the module focuses on the problemof classification; other topics in machine learning are covered by modules in Computer Science.

Aims

• Introduce students to the main problems in machine learning• Introduce students to some of the techniques used for solving problems in data science• Introduce students to neural networks and the main ideas behind “deep learning”• Introduce students to the principal computer packages involved in machine learning

Outline syllabus

• The main problems of data science and machine learning• Data sets and data visualisation• Dimensionality reduction – principal components analysis and introduction to other methods• Supervised learning: the classification problem and discriminant analysis• Regression and classification trees• Ensemble methods and random forests; boosting• Support vector machines• Neural networks and deep learning

Module Format

Lectures 20 Tutorials 0 Practicals 0

Recommended books

C James, Witten, Hastie and Tibshirani, “An Introduction to Statistical Learning” from http://www-bcf.

usc.edu/~gareth/ISL/

C Hastie, Tibshirani and Friedman, “The Elements of Statistical Learning” from https://web.stanford.

edu/~hastie/ElemStatLearn/

C Everitt “An R and S-PLUS Companion to Multivariate Analysis” (Shelfmark 519.535, ISBN 1852338822)

Assessment

Three projects of equal weight.

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MAS370: Sampling Theory and Design of ExperimentsSemester: 2 10 credits

Prerequisites: MAS223 (Statistical Inference and Modelling);MAS367 (Linear and Generalised Linear Models) recommended

Corequisites:Cannot be taken with:Prerequisite for:

Description

The results of sample surveys through opinion polls are commonplace in newspapers and on television. Theobjective of the Sampling Theory section of the module is to introduce several different methods for obtainingsamples from finite populations. Experiments which aim to discover improved conditions are commonplace inindustry, agriculture, etc. The purpose of experimental design is to maximise the information on what is ofinterest with the minimum use of resources. The aim of the Design section is to introduce some of the moreimportant design concepts.

Aims

• To consolidate some previous mathematical and statistical knowledge.• To introduce statistical ideas used in sample surveys and the design of experiments.

Outline syllabus

This course deals with two different areas where the important features are the planning before the data arecollected, and the methods for maximising the information which will be obtained. The results of samplesurveys through opinion polls, etc., are commonplace in newspapers and on television. The Sampling Theorycomponent of the course introduces several different methods for obtaining samples from finite populations andconsiders which method is most appropriate for a given sampling problem. Experiments which aim to discoverimproved conditions are commonplace in industry, agriculture, etc. The purpose of experimental design is tomaximise the information on what is of interest with the minimum use of resources. The Experimental Designcomponent of the course introduces some of the more important design concepts.

Module Format

Lectures 20 Tutorials 0 Practicals 0

Recommended books

B Barnett “Sample Survey: Principles and Methods” (Shelfmark 519.6 (B), ISBN 0340763981)

B Box, Hunter and Hunter “Statistics for Experimenters: Design, Innovation, and Discovery” (Shelfmark519.5(B), ISBN 9780471718130 )

B Morris “Design of Experiments: an Introduction Based on Linear Models” (Shelfmark 001.434 (M),ISBN 9781584889236)

C Atkinson and Donev “Optimum Experimental Designs” (Shelfmark 519.52 (A), ISBN 019929660X)

C Box and Draper “Empirical Model Building and Response Surfaces” (Shelfmark 519.52 (B), ISBN0471810339)

C Cornell “Experiments with Mixtures” (Shelfmark 519.52 (C), ISBN 0471393673)

C Cox and Reid “The Theory of the Design of Experiments” (Shelfmark 519.52 (C), ISBN 158488195X)

C Goos and Jones “Optimal Design of Experiments : A Case Study Approach” (Shelfmark 670.285 (G),ISBN 9780470744611)

Assessment

One formal 2 hour written examination. Exam format: all questions compulsory.

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MAS371: Applied ProbabilitySemester: 2 10 credits

Prerequisites: MAS223 (Statistical Inference and Modelling);MAS275 (Probability Modelling)

Corequisites:Cannot be taken with:Prerequisite for:

Description

This unit will link probability modelling to statistics. It will explore a range of models that can be constructedfor random phenomena that vary in time or space - the evolution of an animal population, for example, or thenumber of cancer cases in different regions of the country. It will illustrate how models are built and how theymight be applied: how likelihood functions for a model may be derived and used to fit the model to data,and how the result may be used to assess model adequacy. Models examined will build on those studied inMAS275.

Aims

• Illustrate the construction of probability models for random phenomena;• Introduce some of the common classes of models for random phenomena;• Illustrate how probability models may be fitted to data;• Discuss applications of fitted models.

Outline syllabus

• Basic techniques: likelihood functions and their properties and use.• Continuous time Markov chains: Introduction; generator matrices; informal coverage of stationary

distributions and convergence.• Inference for stochastic processes: deriving likelihood functions for stochastic processes; fitting models

to data; model criticism.• Applications of Markov chains: birth-death processes; queues.• Point processes: homogeneous and inhomogeneous Poisson processes, spatial and marked point pro-

cesses, inference for point processes.

Module Format

Lectures 20 Tutorials 0 Practicals 0

Recommended books

C Bailey “The Elements of Stochastic Processes with Applications to the Natural Sciences” (Shelfmark519.31 (B))

C Grimmett and Stirzaker “Probability and Random Processes” (Shelfmark 519.2 (G), ISBN 0198572239)

C Guttorp “Stochastic Modeling of Scientific Data” (Shelfmark 519.23 (G), ISBN 0412992817)

C Renshaw “Modelling Biological Populations in Space and Time” (Shelfmark 574.55 (R), ISBN 0521448557)

C Taylor and Karlin “An Introduction to Stochastic Modelling” (Shelfmark 519.2 (T), ISBN 0126848874)

Assessment

One 2 hour written examination.

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MAS372: Time SeriesSemester: 2 10 credits

Prerequisites: MAS223 (Statistical Inference and Modelling)Corequisites:Cannot be taken with:Prerequisite for:

Description

Time series are observations made in time, for which the time aspect is potentially important for understandingand use. The course aims to give an introduction to modern methods of time series analysis and forecastingas applied in economics, engineering and the natural, medical and social sciences. The emphasis will be onpractical techniques for data analysis, though appropriate stochastic models for time series will be introduced asnecessary to give a firm basis for practical modelling. For the implementation of the methods the programminglanguage R will be used.

Aims

• To introduce methods to uncover structure in series of observations made through time.• To illustrate how models for time series may be constructed and studied.• To develop methods to analyse and forecast time series.• To show how these methods are applied to data, and what kinds of conclusion are possible.

Outline syllabus

• Examples of time series. Purposes of analysis. Components (trend, cycle, seasonal, irregular). Station-arity and autocorrelation.

• Approaches to time series analysis. Simple descriptive methods: smoothing, decomposition.• Differencing. Autocorrelation. Probability models for stationary series. Autoregressive models.• Moving average models. Partial autocorrelation. Invertibility. ARMA processes.• ARIMA models for non-stationary series. Identification and fitting. Diagnostics. Ljung-Box statistic,

introduction to forecasting.• State space models. Filtering (Kalman filter), smoothing and forecasting.• Trend and seasonal state space models, time-varying regression. Estimation of hyperparameters, error

analysis.

Module Format

Lectures 20 Tutorials 0 Practicals 0

Recommended books

A Brockwell and Davies “Introduction to Time Series and Forecasting” (Shelfmark 519.36 (B), ISBN0387953515)

A Shumway and Stoffer “Time Series Analysis and its Applications : With R Examples” (Shelfmark 519.55(S) , ISBN 0387293175)

B Chatfield “The Analysis of Time Series : An Introduction” (Shelfmark 519.55 (C) , ISBN 1584883170)

B West and Harrison “Bayesian Forecasting and Dynamic Models” (Shelfmark 519.42 (W), ISBN 0387947256)

Assessment

One formal 2 hour written examination. Format: 3 questions from 3.

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MAS377: Mathematical BiologySemester: 1 10 credits

Prerequisites: MAS110 (Mathematics Core I); MAS111 (Mathematics Core II);MAS222 (Differential Equations)

Corequisites:Cannot be taken with:Prerequisite for:

Description

The course provides an introduction to the mathematical modelling of the dynamics of biological populations.The emphasis will be on deterministic models based on systems of differential equations that encode populationbirth and death rates. Examples will be drawn from a range of different dynamic biological populations, fromthe species level down to the dynamics of molecular populations within cells. Central to the course will be thedynamic consequences of feedback interactions within the populations. In cases where explicit solutions arenot readily obtainable, techniques that give a qualitative picture of the model dynamics (including numericalsimulation) will be used.

Aims

To introduce students to the applications of mathematical techniques in deterministic models for the dynamicsof biological populations.

Outline syllabus

• Population models: Deterministic models; birth and death processes; logistic growth; competitionbetween populations.

• Epidemic models: Compartment models; the SIR model.• Biochemical and Genetic Networks: Mass-action kinetics; simple genetic circuits; genetic switches

and clocks.

Module Format

Lectures 20 Tutorials 0 Practicals 0

Recommended books

B JMurray “Mathematical Biology” (Shelfmark 570.15118 (M), ISBN 9780387952239)

B Ellner and Guckenheimer “Dynamic Models in Biology” (Shelfmark 570.15118 (E), ISBN 9780691125893)

C van den Berg “Mathematical Models of Biological Systems” (Shelfmark 570.15118 (B), ISBN 9780199582181)

Assessment

One formal 2 hour written examination. Format: 3 questions from 4.

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MAS442: Galois TheorySemester: 2 10 credits

Prerequisites: MAS333 (Fields) or MAS438 (Fields)Corequisites:Cannot be taken with:Prerequisite for:

Description

Given a field K (as studied in MAS333/438) one can consider the group G of isomorphisms from K to itself.In the cases of interest, this is a finite group, and there is a tight link (called the Galois correspondence)between the structure of G and the subfields of K. If K is generated over the rationals by the roots of apolynomial f(x), then G can be identified as a group of permutations of the set of roots. One can thenuse the Galois correspondence to help find formulae for the roots, generalising the standard formula for theroots of a quadratic. It turns out that this works whenever the degree of f(x) is less than five. However,the fifth symmetric group lacks certain group-theoretic properties that lie behind these formulae, so there isno analogous method for solving arbitrary quintic equations. The aim of this course is to explain this theory,which is strikingly rich and elegant.

Aims

• To explain the general theory of homomorphisms between fields.• To explain the definition of Galois groups, and to compute them for cyclotomic extensions, and various

extensions of small degree.• To explain the Galois correspondence, and use it to reduce various questions in field theory to easier

questions about finite groups.• To study splitting fields and Galois theory for cubics and quartics, and to explain how they lead to

algorithms for finding roots.

Outline syllabus

• Review of fields and other background• Homomorphisms and field extensions• Splitting fields• Extending homomorphisms; normal field extensions; Galois groups• Examples involving extensions of small degree• Cyclotomic fields and their Galois groups• The Galois correspondence• Cubics and quartics• Extension by radicals and solvability

Module Format

Lectures 20 Tutorials 0 Practicals 0

Recommended books

B Edwards “Galois Theory” (Shelfmark 512.81 (E), ISBN 038790980X)

B Rotman “Galois Theory” (Shelfmark 512.81 (R), ISBN 0387985417)

B Stewart “Galois Theory” (Shelfmark 512.43 (S), ISBN 1584883936)

C King “Beyond the Quartic Equation” (Shelfmark 512.3 (K), ISBN 0817637761)

Assessment

One formal 2.5 hour examination. Format: attempt all questions.

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